ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS

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SARI M., Siap I., Siap V.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.52, no.6, pp.2011-2023, 2015 (SCI-Expanded) identifier identifier

  • 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
  • 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].