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Now showing items 11-20 of 93
A BCH code and a sequence of cyclic codes
(2014)
This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the ...
Encoding through generalized polynomial codes
(2011-08-31)
This paper introduces novel constructions of cyclic codes using semigroup rings instead of polynomial rings. These constructions are applied to define and investigate the BCH, alternant, Goppa, and Srivastava codes. This ...
Encoding through generalized polynomial codes
(2011-08-31)
This paper introduces novel constructions of cyclic codes using semigroup rings instead of polynomial rings. These constructions are applied to define and investigate the BCH, alternant, Goppa, and Srivastava codes. This ...
Constructions of new families of nonbinary CSS codes
(Elsevier Science BvAmsterdamHolanda, 2010)
Alternant and BCH codes over certain rings
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2003-01-01)
Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate ...
Alternant and BCH codes over certain rings
(Springer, 2003-01-01)
Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x(s) - 1 over the unit group of an appropriate ...