环 Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp 上的二次剩余码

doi:10.3969/j.issn.0253-2778.2017.07.008

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (7): 602-609.DOI: 10.3969/j.issn.0253-2778.2017.07.008

环 Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp 上的二次剩余码

钱丽琴，施敏加，SOKLin，平静水

1. 计算智能与信号处理教育部重点实验室, 安徽合肥， 230039; 2. 东南大学移动通信国家重点实验室，江苏南京，210096;  3. 安徽大学数学科学学院, 安徽合肥，230601; 4. 金边皇家学院数学系，柬埔寨; 5. 淮南师范大学经济系, 安徽淮南, 232038

收稿日期:2016-04-30 修回日期:2016-12-30 出版日期:2017-07-31 发布日期:2017-07-31

Quadratic residue codes over Fp+u Fp+ v Fp+uv Fp+v2 Fp+uv2 Fp

QIAN Liqin , SHI Minjia, SOK Lin, PING Jingshui

(1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Hefei 230039, China; 2. National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China; 3. School of Mathematical Sciences, Anhui University, Hefei 230026, China; 4. Department of Mathematics, Royal University of Phnom Penh, Cambodia; 5. School of Finance, Huainan Normal University, Huainan 232001, China

Received:2016-04-30 Revised:2016-12-30 Online:2017-07-31 Published:2017-07-31
Contact: SHI Minjia
About author:QIAN Liqin, female, born in 1991, Master candidate. Research field: Algebraic coding. E-mail: qianliqin_1108@163.com
Supported by:
Supported by National Natural Science Foundation of China (61672036), the Open Research Fund of National Mobile Communications Research Laboratory (2015D11), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities (gxyqZD2016008).

摘要/Abstract

摘要： 设 R= Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp, 其中 u2=1, v3=v, p 是一个奇素数. 研究了环 R 上素长度 n=q 的二次剩余码，其中 q (q≠p) 是一个奇素数且 p 是模 q 的二次剩余.首先研究了环 R 上长度为 n 的循环码, 根据其幂等生成元定义了环 R 上的二次剩余码，进一步讨论了该环上二次剩余码与其扩展码的关系. 最后，为了验证结果的正确性, 给出了 Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp 上二次剩余码的幂等生成元的两种具体形式.

关键词: 循环码, 二次剩余码, 生成幂等元, 对偶码

Abstract: Let R=Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp, where u2=1, v3=v, and p is an odd prime. Quadratic residue codes of prime length n=q over the ring R was investigated, where q (q≠p) is an odd prime such that p is a quadratic residue modulo q. The cyclic codes of length n over R were studied, and then the quadratic residue codes over R in terms of idempotent generators were difined. Moreover, the relation between these codes and their extended codes are discussed. Finally, two specific forms of idempotent generators of quadratic residue codes over  Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp were given to illustrate some results.

Key words: cyclic codes, quadratic residue codes, generating idempotents, dual codes

中图分类号:

O157.4

钱丽琴，施敏加，SOKLin，平静水. 环 Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp 上的二次剩余码[J]. 中国科学技术大学学报, 2017, 47(7): 602-609.

QIAN Liqin , SHI Minjia, SOK Lin, PING Jingshui. Quadratic residue codes over Fp+u Fp+ v Fp+uv Fp+v2 Fp+uv2 Fp[J]. Journal of University of Science and Technology of China, 2017, 47(7): 602-609.

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[5]	储强，朱士信. Zps 上的准循环码[J]. 中国科学技术大学学报, 2013, 43(8): 622-625.

环 Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp 上的二次剩余码

Quadratic residue codes over Fp+u Fp+ v Fp+uv Fp+v2 Fp+uv2 Fp

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