New upper bounds on the number of non-zero weights of constacyclic codes

IF 0.7 3区 数学 Q2 MATHEMATICS
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引用次数: 0

Abstract

For any simple-root constacyclic code C over a finite field Fq, as far as we know, the group G generated by the multiplier, the constacyclic shift and the scalar multiplications is the largest subgroup of the automorphism group Aut(C) of C. In this paper, by calculating the number of G-orbits of C{0}, we give an explicit upper bound on the number of non-zero weights of C and present a necessary and sufficient condition for C to meet the upper bound. Some examples in this paper show that our upper bound is tight and better than the upper bounds in Zhang and Cao (2024) [26]. In particular, our main results provide a new method to construct few-weight constacyclic codes. Furthermore, for the constacyclic code C belonging to two special types, we obtain a smaller upper bound on the number of non-zero weights of C by substituting G with a larger subgroup of Aut(C). The results derived in this paper generalize the main results in Chen et al. (2024) [9].

常环码非零权重数的新上限
本文通过计算 C﹨{0}的 G 轨道数,给出了 C 的非零权重数的明确上界,并提出了 C 满足上界的必要条件和充分条件。本文中的一些例子表明,我们的上界很紧,优于 Zhang 和 Cao (2024) [26] 中的上界。特别是,我们的主要结果提供了一种构造少权常环码的新方法。此外,对于属于两种特殊类型的常环码 C,我们通过用 Aut(C) 的一个较大子群代替 G,得到了较小的 C 非零权重数上限。本文得出的结果概括了 Chen 等人 (2024) [9] 的主要结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Discrete Mathematics
Discrete Mathematics 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
424
审稿时长
6 months
期刊介绍: Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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