Function-correcting codes with homogeneous distance

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-01-13 DOI:10.1016/j.ffa.2026.102791

Huiying Liu, Hongwei Liu

引用次数: 0

Abstract

Function-correcting codes are designed to reduce redundancy of codes when protecting function values of information against errors. As generalizations of Hamming weights and Lee weights over

Z_{4}

, homogeneous weights are used in codes over finite rings. In this paper, we introduce function-correcting codes with homogeneous distance denoted by FCCHDs, which extend function-correcting codes with Hamming distance. We first define D-homogeneous distance codes. We use D-homogeneous distance codes to characterize connections between the optimal redundancy of FCCHDs and lengths of these codes for some matrices D. By these connections, we obtain several bounds of the optimal redundancy of FCCHDs for some functions. In addition, we also construct FCCHDs for homogeneous weight functions and homogeneous weight distribution functions. Specially, redundancies of some codes we construct in this paper reach the optimal redundancy bounds.

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齐次距离函数校正码

功能校正码的设计是为了在保护信息的功能值不受错误影响时减少代码的冗余。作为Z4上的Hamming权和Lee权的推广，齐次权用于有限环上的码。本文引入了用FCCHDs表示的具有齐次距离的功能纠错码，它扩展了具有汉明距离的功能纠错码。首先定义d齐次距离码。我们用d -齐次距离码来描述一些矩阵d的fcchd的最优冗余度和这些码的长度之间的联系，通过这些联系，我们得到了一些函数的fcchd的最优冗余度的几个界。此外，我们还构造了齐次权函数和齐次权分布函数的FCCHDs。特别地，本文构造的一些码的冗余达到了最优冗余界。

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.