Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(6): 2011-2023

Printed November 30, 2015

https://doi.org/10.4134/BKMS.2015.52.6.2011

Copyright © The Korean Mathematical Society.

One-homogeneous weight codes over finite chain rings

Mustafa Sari, Irfan Siap, and Vedat Siap

Yildiz Technical University, Yildiz Technical University, Yildiz Technical University

Abstract

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in \cite{9} from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi \emph{et al.} in \cite{shi2}.

Keywords: linear codes, constant weight codes, gray map, optimal codes

MSC numbers: Primary 94B08, 94B60