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CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON
(World Scientific Publ Co Pte Ltd, 2012-08-01)
It is very well known that algebraic structures have valuable applications in the theory of error-correcting codes. Blake [Codes over certain rings, Inform. and Control 20 (1972) 396-404] has constructed cyclic codes over ...
CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON
(World Scientific Publ Co Pte Ltd, 2012-08-01)
It is very well known that algebraic structures have valuable applications in the theory of error-correcting codes. Blake [Codes over certain rings, Inform. and Control 20 (1972) 396-404] has constructed cyclic codes over ...
Cyclic codes through B[X;(a/b)Z_0, with (a/b) in Q^{+} and b=a+1, and Encoding
(2012)
Let B[X; S] be a monoid ring with any fixed finite unitary commutative ring B and is the monoid S such that b = a + 1, where a is any positive integer. In this paper we constructed cyclic codes, BCH codes, alternant codes, ...
CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON
(World Scientific Publ Co Pte Ltd, 2014)
A Note on Linear Codes over Semigroup Rings
(2011)
In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with ...
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 ...
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 ...
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) ...
Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding
(Pergamon-Elsevier B.V. Ltd, 2014)