Shortest-path and antichain metrics

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-26 DOI:10.1016/j.ffa.2025.102658

Mahir Bilen Can, Dillon Montero

引用次数: 0

Abstract

In this paper, we introduce two new metrics for error-correcting codes that extend the classical Hamming metric. The first, called the shortest-path metric, coincides with the Niederreiter-Rosenbloom-Tsfasman (NRT) metric when the underlying poset is a disjoint union of equal-length chains. The second, called the antichain metric, is shown to align with the b-symbol Hamming weight under the same poset structure. We explore analogs of maximum distance separable (MDS) codes and perfect codes for both metrics and determine the corresponding weight enumerator polynomials. Additionally, we establish criteria for when the antichain metric yields one-weight perfect codes.

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最短路径和反链度量

本文引入了两个新的纠错码度量，它们是对经典汉明度量的扩展。第一个称为最短路径度量，当底层偏序集是等长链的不相交并时，它与niederreiter - rosenbloomm - tsfasman （NRT）度量一致。第二种称为反链度规，在相同的偏置结构下与b符号汉明权对齐。我们探索了最大距离可分离码和完美码的类似物，并确定了相应的权重枚举多项式。此外，我们还建立了反链度量产生单权完美码的准则。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.