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A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
(2013-09-01)
For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of ...
Construction and decoding of BCH codes over finite commutative rings
(1999-01-01)
BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of 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 ...
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 ...
Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding
(Pergamon-Elsevier B.V. Ltd, 2011-08-01)
For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) ...