Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS

  • SARI, MUSTAFA (Department of Mathematics Yildiz Technical University) ;
  • SIAP, IRFAN (Department of Mathematics Yildiz Technical University) ;
  • SIAP, VEDAT (Department of Mathematical Engineering Yildiz Technical University)
  • Received : 2014.10.14
  • Published : 2015.11.30
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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].

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References

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