ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.52, no.6, pp.2011-2023, 2015 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 52 Issue: 6
- Publication Date: 2015
- Doi Number: 10.4134/bkms.2015.52.6.2011
- Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2011-2023
- Keywords: linear codes, constant weight codes, gray map, optimal codes, P-ARY CODES, LINEAR CODES
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
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 [7] 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 et al. in [17].