Classification of cyclic codes over a non-Galois chain ring Z_p[u]/

Kim Boran; Lee Yoonjin; Doo Jisoo

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Classification of cyclic codes over a non-Galois chain ring Z_p[u]/

机译：非Galois链环Z_p [u] /上的循环码分类

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摘要

We explicitly determine generators of cyclic codes over a non-Galois finite chain ring Z(p)[u]/< u(3)> of length p(k), where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of Z(p)[u]/< u(3)> and four types of non-principal ideals of Z(p)[u]/< u(3)>, which are associated with cyclic codes over Z(p)[u]/< u(3)> of length p(k). We then obtain a mass formula for cyclic codes over Z(p)[u]/< u(3)> of length p(k). (C) 2019 Elsevier Inc. All rights reserved.

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来源
《Finite fields and their applications》 |2019年第9期|208-237|共30页
作者
Kim Boran; Lee Yoonjin; Doo Jisoo;
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作者单位

Ewha Womans Univ Inst Math Sci Seoul 03760 South Korea;

Ewha Womans Univ Dept Math Seoul 03760 South Korea;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Cyclic code; Mass formula; Finite chain ring;

机译：循环码;质量公式;有限链环;

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1. Classification of cyclic codes over a non-Galois chain ring Z_p[u]/ [J] . Kim Boran, Lee Yoonjin, Doo Jisoo Finite fields and their applications . 2019,第Sepa期

机译：非Galois链环Z_p [u] /上的循环码分类
2. Classification of self-dual cyclic codes over the chain ring Z_p[u]/〈u~3〉 [J] . Kim Boran, Lee Yoonjin Designs, Codes and Crytography . 2020,第10期

机译：在链环Z_P [U] / 上的自双循环码分类
3. On cyclic codes over the ring Z_p[u]/ [J] . Abhay Kumar Singh, Pramod Kumar Kewat Designs, Codes and Crytography . 2015,第1期

机译：在环Z_p [u] / 上的循环码上
4. Quantum codes from cyclic codes over a class of nonchain rings [C] . Sari Mustafa, Siap Irfan International Conference on Modeling, Simulation and Applied Optimization . 2015

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5. New quasi-cyclic and quasi-twisted codes and an optimal family of polynomial codes. [D] . Aydin, Nuh. 2002

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7. Classification of All Cyclic Codes over the Finite Chain Ring Z4+wZ4 of Length 4s [O] . Xiaofang Xu, Shujie Yun 2013

机译：在长度4s的有限链环Z4 + WZ4上的所有循环码的分类

Classification of cyclic codes over a non-Galois chain ring Z_p[u]/

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