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.
Mustafa Sari, Irfan Siap, and Vedat Siap
Yildiz Technical University, Yildiz Technical University, Yildiz Technical University
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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