有限域上斜λ-常循环码中互补对偶码的存在性及其性质

doi:10.3976/j.issn.1002-4026.2019.03.013

山东科学 ›› 2019, Vol. 32 ›› Issue (3): 85-89.doi: 10.3976/j.issn.1002-4026.2019.03.013

有限域上斜λ-常循环码中互补对偶码的存在性及其性质

赵鹏程，李秀丽^*

青岛科技大学数理学院，山东青岛 266061

收稿日期:2018-08-12 出版日期:2019-06-20 发布日期:2019-06-01
作者简介:赵鹏程（1995—），男，硕士生，研究方向为组合设计与编码理论。
基金资助:
国家自然科学基金（11671235）；青岛市博士后基金（861605040007）

Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields

ZHAO Peng-cheng, LI Xiu-li^*

College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

Received:2018-08-12 Online:2019-06-20 Published:2019-06-01

摘要/Abstract

摘要： 线性互补对偶码（LCD码）有良好的相关特性和正交特性，是编码理论研究的热点之一。在普通多项式环的基础上引入了自同构映射，得到有限域上的斜λ-常循环码，研究了有限域上斜λ-常循环码中互补对偶码的存在性及其性质，并且讨论了有限域上斜循环码中LCD码的计数问题。

关键词: 线性互补对偶码, 多项式环, 自同构映射, 斜λ-常循环码

Abstract: Linear complementary-dual codes (LCD codes) have good correlation and orthogonal properties, which are one of the hot topics in coding theory research. In this paper, automorphism maps were introduced based on the ordinary polynomial ring, and the skew λ-cyclic codes over finite fields were obtained. We studied the existence and properties of the complementary-dual codes in the skew λ-cyclic codes over finite fields. Moreover, the counting problem of LCD codes in the skew λ-cyclic codes over finite fields was also discussed.

Key words: linear complementarity-dual codes, polynomial rings, automorphism mapping, skew λ-cyclic codes

中图分类号:

O236.2

赵鹏程, 李秀丽. 有限域上斜λ-常循环码中互补对偶码的存在性及其性质[J]. 山东科学, 2019, 32(3): 85-89.

ZHAO Peng-cheng, LI Xiu-li. Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields[J]. Shandong Science, 2019, 32(3): 85-89.

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有限域上斜λ-常循环码中互补对偶码的存在性及其性质

Existence and properties of complementary-dual codes in skew λ-cyclic codes over finite fields

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