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ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS
SARI, MUSTAFA,SIAP, IRFAN,SIAP, VEDAT Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
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].
ONE-HOMOGENEOUS WEIGHT CODES OVER FINITE CHAIN RINGS
Mustafa Sari,Irfan Siap,Vedat Siap 대한수학회 2015 대한수학회보 Vol.52 No.6
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].
Ozen, Mehmet,Shi, Minjia,Siap, Vedat Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.