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Hauptverfasser:	Liu, Huiying, Liu, Hongwei
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Information Theory
Online-Zugang:	https://arxiv.org/abs/2507.03332
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

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author	Liu, Huiying Liu, Hongwei
author_facet	Liu, Huiying Liu, Hongwei
contents	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 $ \mathbb{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 $-homogenous 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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2507_03332
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Function-Correcting Codes with Homogeneous Distance Liu, Huiying Liu, Hongwei Information Theory 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 $ \mathbb{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 $-homogenous 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.
title	Function-Correcting Codes with Homogeneous Distance
topic	Information Theory
url	https://arxiv.org/abs/2507.03332

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