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On Codes with Distances $$d$$ and $$n$$
Problems of Information Transmission ( IF 1.2 ) Pub Date : 2023-01-10 , DOI: 10.1134/s0032946022040068 P. Boyvalenkov , K. Delchev , V. A. Zinoviev , D. V. Zinoviev
中文翻译:
关于距离为 $$d$$ 和 $$n$$ 的代码
更新日期:2023-01-11
Problems of Information Transmission ( IF 1.2 ) Pub Date : 2023-01-10 , DOI: 10.1134/s0032946022040068 P. Boyvalenkov , K. Delchev , V. A. Zinoviev , D. V. Zinoviev
We enumerate all \(q\)-ary additive (in particular, linear) block codes of length \(n\) and cardinality \(N\ge q^2\) with exactly two distances: \(d\) and \(n\). For arbitrary codes of length \(n\) with distances \(d\) and \(n\), we obtain upper bounds on the cardinality via linear programming and using relationships to 2-distance sets on a Euclidean sphere.
中文翻译:
关于距离为 $$d$$ 和 $$n$$ 的代码
我们枚举长度为\(n\)和基数为\(N\ge q^2\)的所有\(q\)元加法(特别是线性)块代码,恰好有两个距离:\(d\)和\ (n\)。对于长度为\(n\)且距离为\(d\)和\(n\)的任意代码,我们通过线性规划并使用与欧几里德球体上的 2 距离集的关系获得基数的上限。