The symbol-pair distance distribution of repeated-root cyclic codes over $\mathbb{F}_{p^m}$

Shixin Zhu; Zhonghua Sun; Liqi Wang

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arXiv · 1607.01887

The symbol-pair distance distribution of repeated-root cyclic codes over $\mathbb{F}_{p^m}$

Shixin Zhu·Zhonghua Sun·Liqi Wang

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Abstract

Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over $\mathbb{F}_{p^m}$. The exact symbol-pair distances of all cyclic codes of such length are determined.

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Shixin Zhu, Zhonghua Sun, Liqi Wang. 2016-07-07. The symbol-pair distance distribution of repeated-root cyclic codes over $\mathbb{F}_{p^m}$. https://arxiv.org/abs/1607.01887

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