ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS


SARI M. , Siap I. , Siap V.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.52, ss.2011-2023, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 52 Konu: 6
  • Basım Tarihi: 2015
  • Doi Numarası: 10.4134/bkms.2015.52.6.2011
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayısı: ss.2011-2023

Özet

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].