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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 and decoding of a sequence of BCH codes
(2012-01-01)
The BCH code C (respectively, C) of length n over a local ring Z pk (respectively, ℤp) is an ideal in the ring (Equation Presented) (respectively, (Equation Presented) which is generated by a monic polynomial that divides ...
Alternant and BCH codes over certain rings
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2003)
Alternant and BCH codes over certain rings
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2014)
Construction and decoding of BCH Codes over finite commutative rings
(Elsevier Science IncNew YorkEUA, 1999)
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, ...
Linear codes over finite local rings in a chain
(2012)
For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) ...