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Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Bo Yang, Kangkang He, Xiangyong Zeng, Zibi Xiao
Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower
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Constructing linked systems of relative difference sets via Schur rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Mikhail Muzychuk, Grigory Ryabov
In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems sharing the same grading group. Further, we generalize the Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we construct new linked system of RDSs
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Fast decoding of lifted interleaved linearized Reed–Solomon codes for multishot network coding Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Hannes Bartz, Sven Puchinger
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Lengths of divisible codes: the missing cases Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-13 Sascha Kurz
A linear code C over \({\mathbb {F}}_q\) is called \(\Delta \)-divisible if the Hamming weights \({\text {wt}}(c)\) of all codewords \(c \in C\) are divisible by \(\Delta \). The possible effective lengths of \(q^r\)-divisible codes have been completely characterized for each prime power q and each non-negative integer r in Kiermaier and Kurz (IEEE Trans Inf Theory 66(7):4051–4060, 2020). The study
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New constructions of signed difference sets Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-10 Zhiwen He, Tingting Chen, Gennian Ge
Signed difference sets have interesting applications in communications and coding theory. A \((v,k,\lambda )\)-difference set in a finite group G of order v is a subset D of G with k distinct elements such that the expressions \(xy^{-1}\) for all distinct two elements \(x,y\in D\), represent each non-identity element in G exactly \(\lambda \) times. A \((v,k,\lambda )\)-signed difference set is a generalization
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Algebraic properties of the maps $$\chi _n$$ Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-10 Jan Schoone, Joan Daemen
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Jacobi polynomials for the first-order generalized Reed–Muller codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-08 Ryosuke Yamaguchi
In this paper, we give the Jacobi polynomials for first-order generalized Reed–Muller codes. We show as a corollary the nonexistence of combinatorial 3-designs in these codes.
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Anonymous attribute-based broadcast encryption with hidden multiple access structures Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-06 Tran Viet Xuan Phuong
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Ovoids of Q(6, q) of low degree Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-06 Daniele Bartoli, Nicola Durante, Giovanni Giuseppe Grimaldi
Ovoids of the parabolic quadric Q(6, q) of \(\textrm{PG}(6,q)\) have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q(6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q(6, q) two polynomials \(f_1(X,Y,Z)\), \(f_2(X,Y,Z)\) can be associated. In
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On the size distribution of the fixed-length Levenshtein balls with radius one Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-05 Geyang Wang, Qi Wang
The fixed-length Levenshtein (FLL) distance between two words \(\varvec{x}, \varvec{y}\in \mathbb {Z}_m^n\) is the smallest integer t such that \(\varvec{x}\) can be transformed to \(\varvec{y}\) by t insertions and t deletions. The size of a ball in the FLL metric is a fundamental yet challenging problem. Very recently, Bar-Lev, Etzion, and Yaakobi explicitly determined the minimum, maximum and average
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Special overlarge sets of Kirkman triple systems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-05 Juanjuan Xu, Lijun Ji
A Steiner quadruple system of order \(v+1\) with resolvable derived designs (every derived Steiner triple system of order v at a point is resolvable), abbreviated as RDSQS\((v+1)\), has been used to construct a large set of Kirkman triple systems of order 3v. In this paper, an RDSQS\((v+1)\) is reduced to an overlarge set of Kirkman triple systems of order v with an additional property (OLKTS\(^+(v)\))
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Combinatorial constructions of optimal low-power error-correcting cooling codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-04 Shuangqing Liu, Lijun Ji
High temperatures have dramatic negative effects on interconnect performance. In a bus, whenever the state transitions from “0” to “1”, or “0” to “1”, joule heating causes the temperature to rise. A low-power error-correcting cooling (LPECC) code, introduced in Chee et al. (IEEE Trans Inf Theory 64:3062–3085, 2018), is a coding scheme which can be used to control the peak temperature, the average power
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Construction of quantum codes from multivariate polynomial rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-02 Cong Yu, Shixin Zhu, Fuyin Tian
In this paper, we use multivariate polynomial rings to construct quantum error-correcting codes (QECCs) via Hermitian construction. We establish a relation between linear codes and ideals of multivariate polynomial rings. We give a necessary and suffcient condition for a multivariate polynomial to generate a Hermitian dual-containing code. By comparing with the literatures in recent years, we construct
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Optimal binary signed-digit representations of integers and the Stern polynomial Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-02 Laura Monroe
The binary signed-digit (BSD) representation of integers is used for efficient integer computation in various settings. The Stern polynomial is a polynomial extension of the well-studied Stern diatomic sequence. In this paper, we show previously unknown connections between BSD integer representations and the Stern polynomial. We then exploit these connections to devise a fast algorithm to count optimal
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Preimage attacks on reduced-round Ascon-Xof Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-30
Abstract Ascon, a family of algorithms that supports authenticated encryption and hashing, has been selected as the new standard for lightweight cryptography in the NIST Lightweight Cryptography Project. Ascon’s permutation and authenticated encryption have been actively analyzed, but there are relatively few analyses on the hashing. In this paper, we concentrate on preimage attacks on Ascon-Xof. We
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Families of quadratic sets on the Klein quadric Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-30 Bart De Bruyn
Consider the Klein quadric \(Q^+(5,q)\) in \(\text{ PG }(5,q)\). A set of points of \(Q^+(5,q)\) is called a quadratic set if it intersects each plane \(\pi \) of \(Q^+(5,q)\) in a possibly reducible conic of \(\pi \), i.e. in a singleton, a line, an irreducible conic, a pencil of two lines or the whole of \(\pi \). A quadratic set is called good if at most two of these possibilities occur as \(\pi
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Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-29
Abstract We provide classification results for translation generalized quadrangles of order less than or equal to 64, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in \(\textrm{PG}(3n-1,2)\) , for \(n=3,4\) , and that of the pseudo-ovals in \(\textrm{PG}(3n-1,q)\) , for \(n=5,6\) , such that one of the associated projective planes
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Classification of semiregular relative difference sets with $$\gcd (\lambda ,n)=1$$ attaining Turyn’s bound Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Ka Hin Leung, Bernhard Schmidt, Tao Zhang
Suppose a \((\lambda n,n,\lambda n, \lambda )\) relative difference set exists in an abelian group \(G=S\times H\), where \(|S|=\lambda \), \(|H|=n^2\), \(\gcd (\lambda ,n)=1\), and \(\lambda \) is self-conjugate modulo \(\lambda n\). Then \(\lambda \) is a square, say \(\lambda =u^2\), and \(\exp (S)\) divides u by Turyn’s exponent bound. We classify all such relative difference sets with \(\exp (S)=u\)
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Efficient secure multi-party computation for proof of custody in Ethereum sharding Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Yuxin Tong, Xiang Xie, Kang Yang, Rui Zhang, Rui Xue
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PERK: compact signature scheme based on a new variant of the permuted kernel problem Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Slim Bettaieb, Loïc Bidoux, Victor Dyseryn, Andre Esser, Philippe Gaborit, Mukul Kulkarni, Marco Palumbi
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CCA security for contracting (quasi-)Feistel constructions with tight round complexity Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-23 Chun Guo, Ling Song
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On Bose distance of a class of BCH codes with two types of designed distances Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-19 Chunyu Gan, Chengju Li, Haifeng Qian, Xueying Shi
BCH codes are an interesting class of cyclic codes with good error-correcting capability and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Let \(\mathbb {F}_q\) be the finite field of size q and \(n=q^m-1\), where m is a positive integer. Let \(\mathcal C_{(q, m, \delta )}\) be the primitive narrow-sense BCH codes of length n over
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Negacyclic BCH codes of length $$\frac{q^{2m}-1}{q+1}$$ and their duals Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-19 Zhonghua Sun, Xinyue Liu, Shixin Zhu, Yongsheng Tang
Negacyclic BCH codes are an important subclass of negacyclic codes and have good parameters. Inspired by the recent work on cyclic codes published in Wu et al. (Finite Fields Appl 60:101581, 2019), the objective of this paper is to investigate the parameters of the narrow-sense negacyclic BCH codes of length \(n=\frac{q^{2m}-1}{q+1}\) over \({\textrm{GF}}(q)\), where q is an odd prime power. For \(2\le
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Balanced reconstruction codes for single edits Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-16
Abstract Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai et al. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is to design codes with sizes as large as possible, such that every codeword can be uniquely reconstructed from any N distinct noisy reads, where N is fixed. In this
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Impossibility of efficient information-theoretic fuzzy extraction Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-14 Benjamin Fuller
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Monomial isomorphism for tensors and applications to code equivalence problems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12
Abstract Starting from the problem of d-tensor isomorphism (d- \(\textsf {TI}\) ), we study the relation between various code equivalence problems in different metrics. In particular, we show a reduction from the sum-rank metric ( \(\textsf {CE}_{\textsf {sr}}\) ) to the rank metric ( \(\textsf {CE}_{\textsf {rk}}\) ). To obtain this result, we investigate reductions between tensor problems. We define
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Efficient computation of $$(2^n,2^n)$$ -isogenies Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12 S. Kunzweiler
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Square root computation in finite fields Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12 Ebru Adiguzel-Goktas, Enver Ozdemir
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Some constructions and existence conditions for Hermitian self-dual skew codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-10
Abstract In this paper, we first consider the existence conditions, the construction and the enumeration of Hermitian self-dual \(\theta \) -cyclic and \(\theta \) -negacyclic codes over \(\mathrm{I\hspace{-2.10007pt}F}_{p^2}\) , where p is a prime number and \(\theta \) is the Frobenius automorphism over \(\mathrm{I\hspace{-2.10007pt}F}_{p^2}\) . We then give necessary and sufficient conditions for
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MDS codes with l-Galois hulls of arbitrary dimensions Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-09 Liqin Qian, Xiwang Cao, Xia Wu, Wei Lu
The hull of a linear code is defined to be the intersection of the code and its dual, and was originally introduced to classify finite projective planes. The objective of this paper is to construct some MDS codes with l-Galois hulls of arbitrary dimensions by using the generalized Reed–Solomon codes over finite fields with regard to l-Galois inner product. We give a general construction theorem and
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Compressed M-SIDH: an instance of compressed SIDH-like schemes with isogenies of highly composite degrees Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05 Kaizhan Lin, Jianming Lin, Shiping Cai, Weize Wang, Chang-An Zhao
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Extremal regular graphs and hypergraphs related to fractional repetition codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05
Abstract Fractional repetition codes (FRCs) are a special family of storage codes with the repair-by-transfer property in distributed storage systems. Constructions of FRCs are naturally related to combinatorial designs, graphs, and hypergraphs. In this paper, we consider an extremal problem on regular graphs related to FRCs where each packet is stored on \(\rho =2\) nodes. The problem asks for the
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Linear codes associated to determinantal varieties in the space of hermitian matrices Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05 Kanchan Singh, Ritesh Kumar Pathak, Sheo Kumar Singh
We introduce a new class of linear codes over a finite field associated to determinantal varieties in the space of hermitian matrices and determine their length, dimension and minimum distance along with the weight spectrum.
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Large Hermitian hull GRS codes of any given length Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04 Hao Chen
The construction of Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes of many specific lengths and large dimensions has been an active topic. The construction of Euclidean self-dual GRS codes and twisted generalized Reed-Solomon (TGRS) codes attracts some attentions. In this paper, we construct GRS \([n, k, n-k+1]_{q^2}\) codes (thus MDS codes) over \(\textbf{F}_{q^2}\) of the arbitrary
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Twisted skew G-codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04 Angelot Behajaina, Martino Borello, Javier de la Cruz, Wolfgang Willems
In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are in most cases algebras over a finite field, allow us to retrieve many of the well-known codes. The presentation, given here, unifies the concept of group codes, twisted group codes and skew group codes.
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Combining MILP modeling with algebraic bias evaluation for linear mask search: improved fast correlation attacks on SNOW Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04
Abstract The Mixed Integer Linear Programming (MILP) technique has been widely applied in the realm of symmetric-key cryptanalysis. In this paper, we propose a new bitwise breakdown MILP modeling strategy for describing the linear propagation rules of modular addition-based operations. We apply such new techniques to cryptanalysis of the SNOW stream cipher family and find new linear masks: we use the
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A conceptually simple and generic construction of plaintext checkable encryption in the standard model Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-24
Abstract Plaintext-checkable encryption (PCE) can support searches over ciphertext by directly using plaintext. The functionality of a search is modeled by a specific check algorithm that takes a pair of target plaintext and ciphertext as input and returns 1 if the correct decryption result of the ciphertext is identical to the target plaintext. A trivial solution is to use an existing scheme (e.g
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Leakage-resilient $$\textsf {IBE} $$ / $$\textsf {ABE} $$ with optimal leakage rates from lattices Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-24 Qiqi Lai, Feng-Hao Liu, Zhedong Wang
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Self-dual codes from a block matrix construction characterised by group rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-22 Adam Michael Roberts
We give a new technique for constructing self-dual codes based on a block matrix whose blocks arise from group rings and orthogonal matrices. The technique can be used to construct self-dual codes over finite commutative Frobenius rings of characteristic 2. We give and prove the necessary conditions needed for the technique to produce self-dual codes. We also establish the connection between self-dual
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On the sequential indifferentiability of the Lai–Massey construction Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-17 Chun Guo, Yiyuan Luo, Chenyu Xiao
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Using alternating de Bruijn sequences to construct de Bruijn tori Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-06
Abstract A de Bruijn torus is the two dimensional generalization of a de Bruijn sequence. While methods exist to generate these tori, only a few methods of construction are known. We present a novel method to generate de Bruijn tori with rectangular windows by combining two variants of de Bruijn sequences.
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A recursive construction of doubly resolvable Steiner quadruple systems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Zhaoping Meng, Qingling Gao, Zhanggui Wu
Two resolutions of the same 3-design are said to be orthogonal when each parallel class of one resolution has at most one block in common with each parallel class of the other resolution. If a Steiner quadruple system has two mutually orthogonal resolutions, the design is called doubly resolvable and denoted by DRSQS. In this paper, we define almost doubly resolvable candelabra quadruple system and
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On the parameters of extended primitive cyclic codes and the related designs Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Haode Yan, Yanan Yin
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight in this code support a 2-design. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined and the parameters of the related 2-designs are also given. Moreover, we prove
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Perfect mixed codes from generalized Reed–Muller codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Alexander M. Romanov
In this paper, we propose a new method for constructing 1-perfect mixed codes in the Cartesian product \(\mathbb {F}_{n} \times \mathbb {F}_{q}^n\), where \(\mathbb {F}_{n}\) and \(\mathbb {F}_{q}\) are finite fields of orders \(n = q^m\) and q. We consider generalized Reed-Muller codes of length \(n = q^m\) and order \((q - 1)m - 2\). Codes whose parameters are the same as the parameters of generalized
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Infinite families of minimal binary codes via Krawtchouk polynomials Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-22 Xiaoni Du, René Rodríguez, Hao Wu
Linear codes play a crucial role in various fields of engineering and mathematics, including data storage, communication, cryptography, and combinatorics. Minimal linear codes, a subset of linear codes, are particularly essential for designing effective secret sharing schemes. In this paper, we introduce several classes of minimal binary linear codes by carefully selecting appropriate Boolean functions
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Predicate encryption with selective-opening security for receivers: formal definition, generic construction, and concrete instantiations for several primitives Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-20 Yi-Fan Tseng, Zi-Yuan Liu, Raylin Tso
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Sperner’s theorem for non-free modules over finite chain rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-20 Ivan Landjev, Emiliyan Rogachev
We prove Sperner-type theorems for the partially ordered set \(\mathcal {P}_M\) of all submodules of a non-free finitely generated module \({}_RM\) over a finite chain ring R. We demonstrate that the partially ordered set \(\mathcal {P}_M\) is not necessarily of Sperner type and solve the problem for modules of shape \(2^11^n\). This result is further generalized for modules of shape \(m^11^n\) over
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In search of maximum non-overlapping codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08 Lidija Stanovnik, Miha Moškon, Miha Mraz
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Hardness estimates of the code equivalence problem in the rank metric Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08
Abstract In this paper, we analyze the hardness of the Matrix Code Equivalence (MCE) problem for matrix codes endowed with the rank metric, and provide the first algorithms for solving it. We do this by making a connection to another well-known equivalence problem from multivariate cryptography—the Isomorphism of Polynomials (IP). Under mild assumptions, we give tight reductions from MCE to the homogenous
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New constructions of constant dimension subspace codes with large sizes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08 Yun Li, Hongwei Liu, Sihem Mesnager
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension
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Improved bounds for codes correcting insertions and deletions Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-07 Kenji Yasunaga
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Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-29 Alexander L. Gavrilyuk, Vladislav V. Kabanov
In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph \(\textsf{Sp}(2d,q)\). In this paper, we determine the parameters of strongly regular graphs which admit a decomposition
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Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectra Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 Suman Dutta, Subhamoy Maitra
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On a class of permutation rational functions involving trace maps Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27
Abstract Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility
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Harmonic Tutte polynomials of matroids II Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 Thomas Britz, Himadri Shekhar Chakraborty, Reina Ishikawa, Tsuyoshi Miezaki, Hopein Christofen Tang
In this work, we introduce the harmonic generalization of the m-tuple weight enumerators of codes over finite Frobenius rings. A harmonic version of the MacWilliams-type identity for m-tuple weight enumerators of codes over finite Frobenius ring is also given. Moreover, we define the demi-matroid analogue of well-known polynomials from matroid theory, namely Tutte polynomials and coboundary polynomials
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On the (in)security of optimized Stern-like signature schemes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 André Chailloux, Simona Etinski
Stern’s signature scheme is a historically important code-based signature scheme. A crucial optimization of this scheme is to generate pseudo-random vectors and permutation instead of random ones, and most proposals that are based on Stern’s signature use this optimization. However, its security has not been properly analyzed, especially when we use deterministic commitments. In this article, we study
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Construction of self-orthogonal $$\mathbb {Z}_{2^k}$$ -codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-19
Abstract In this paper we give three constructions of cyclic self-orthogonal codes over \(\mathbb {Z}_{2^k}\) , for \(k\ge 3,\) from Boolean functions on n variables. The first construction for each k, \(3\le k\le n,\) yields a self-orthogonal \(\mathbb {Z}_{2^k}\) -code of length \(2^{n+2}\) with all Euclidean weights divisible by \(2^{k+1}.\) In the remaining two constructions, for each even n and
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Weierstrass semigroups, pure gaps and codes on function fields Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-19 Alonso S. Castellanos, Erik A. R. Mendoza, Luciane Quoos
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Optimal binary and ternary locally repairable codes with minimum distance 6 Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-15 Wenqin Zhang, Yuan Luo, Lele Wang
A locally repairable code (LRC) is a code that can recover any symbol of a codeword by reading at most \(r \) other symbols, denoted by \(r \)-LRC. In this paper, we study binary and ternary linear LRCs with disjoint repair groups and minimum distance \(d \) = 6. Using the intersection subspaces technique, we explicitly construct dimensional optimal LRCs. First, based on the intersection subspaces
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Codes on subgroups of weighted projective tori Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-09 Mesut Şahin, Oğuz Yayla