Good p-ary quasic-cyclic codes from cyclic codes over F p+υF p

Minjia Shi; Shanlin Yang; Shixin Zhu

doi:10.1007/s11424-012-0076-7

Good p-ary quasic-cyclic codes from cyclic codes over F _p+υF _p

Minjia Shi
, Shanlin Yang
, Shixin Zhu

科研成果: 期刊稿件 › 文章 › 同行评审

23 引用（Scopus）

摘要

This paper introduces a Gray map from (F _p+υF _p) to F _p ²ⁿ and describes the relationship between codes over F _p+υF _p and their Gray images. The authors prove that every cyclic code of arbitrary length n over F _p+υF _p is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.

源语言	英语
页（从-至）	375-384
页数	10
期刊	Journal of Systems Science and Complexity
卷	25
期	2
DOI	https://doi.org/10.1007/s11424-012-0076-7
出版状态	已出版 - 4月 2012
已对外发布	是

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abstract = "This paper introduces a Gray map from (F p+υF p) to F p 2n and describes the relationship between codes over F p+υF p and their Gray images. The authors prove that every cyclic code of arbitrary length n over F p+υF p is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.",

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AU - Yang, Shanlin

AU - Zhu, Shixin

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N2 - This paper introduces a Gray map from (F p+υF p) to F p 2n and describes the relationship between codes over F p+υF p and their Gray images. The authors prove that every cyclic code of arbitrary length n over F p+υF p is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.

AB - This paper introduces a Gray map from (F p+υF p) to F p 2n and describes the relationship between codes over F p+υF p and their Gray images. The authors prove that every cyclic code of arbitrary length n over F p+υF p is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.

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KW - Gray image

KW - generator matrix

KW - linear code

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ER -

Good p-ary quasic-cyclic codes from cyclic codes over F p+υF p

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Good p-ary quasic-cyclic codes from cyclic codes over F _p+υF _p