谐波高权重和扩展权重枚举数

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2025-06-27 DOI:10.1016/j.jcta.2025.106090

Thomas Britz , Himadri Shekhar Chakraborty , Tsuyoshi Miezaki

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引用次数: 0

摘要

本文给出了有限域上众所周知的码多项式的调和推广，即高权枚举数和扩展权枚举数，并推导了这些权枚举数之间的对应关系。此外，我们给出了格林定理在高阶方程上的调和推广。扩展)权重枚举数。作为Greene型定理的一个应用，我们给出了有限域上码的调和高权枚举数的macwilliams型恒等式。最后，我们利用这个新恒等式给出了有限域上线性码的子码支持的Assmus-Mattson定理的一个新的证明。

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Harmonic higher and extended weight enumerators

In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight enumerators. Moreover, we present the harmonic generalization of Greene's Theorem for the higher (resp. extended) weight enumerators. As an application of this Greene's-type theorem, we provide the MacWilliams-type identity for harmonic higher weight enumerators of codes over finite fields. Finally, we use this new identity to give a new proof of the Assmus-Mattson Theorem for subcode supports of linear codes over finite fields using harmonic higher weight enumerators.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.