Abstract

The homogeneous weight (metric) is useful in the construction of codes over a ring of integers \(\mathbb {Z}_{p^l}\) (p prime and \(l \ge 1\) an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be \(\mathbb {Z}_{4}\) . This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of n-tuples over \(\mathbb {Z}_{p^l}\) . Necessary and sufficient conditions for existence of an (n, k) linear code over \(\mathbb {Z}_{p^l}\) correcting the error patterns with respect to the homogeneous weight are derived.

中文翻译：

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具有均匀距离的纠正重复突发的线性码

摘要

齐次权重（度量）对于在整数环\(\mathbb {Z}_{p^l}\)（p素数和\(l \ge 1\)整数）上构建代码很有用。当环被视为有限域时，它成为汉明权重；当环被视为\(\mathbb {Z}_{4}\)时，它成为李权重。本文提出了\(\mathbb {Z}_{p^l}\)上n元组代码空间中突发和重复突发错误的均匀权重分布和总均匀权重。推导了在\(\mathbb {Z}_{p^l}\)上存在 ( n ,  k ) 线性码来校正关于齐次权重的错误模式的充分必要条件。