关于从$$\omega $$ -circulant平衡广义称重矩阵推导出的最优恒权码

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-05-14 DOI:10.1007/s10623-024-01414-w

Hadi Kharaghani, Thomas Pender, Vladimir Tonchev

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引用次数: 0

摘要

平衡广义权重矩阵被用来构造最优恒权码，这些恒权码与由经典单纯形码派生的码在单体上是不等价的。更重要的是，这些编码可以假定完全由单个编码词的（\omega \）移位产生，其中（$\omega $是伽罗瓦域的基元。通过投影到字母集的子群上，还衍生出了其他恒权码。这些编码也被证明是最优的。

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On optimal constant weight codes derived from $$\omega $$ -circulant balanced generalized weighing matrices

Balanced generalized weight matrices are used to construct optimal constant weight codes that are monomially inequivalent to codes derived from the classical simplex codes. What’s more, these codes can be assumed to be generated entirely by $\omega $-shifts of a single codeword where $\omega $ is a primitive element of a Galois field. Additional constant weight codes are derived by projecting onto subgroups of the alphabet sets. These too are shown to be optimal.

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.