One-homogeneous weight codes over finite chain rings
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 2011-2023
https://doi.org/10.4134/BKMS.2015.52.6.2011
Published online November 30, 2015
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
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