Ascending chain of semigroup rings and encoding

Let B be any finite commutative ring with identity. · · · ⊂ B[X; 1ak Z0] · · · ⊂ B[X; a12 Z0] ⊂ B[X; a1 Z0], where a ∈ {2, 3, 5, 7, · · ·}, k ≥ 1, is the descending chain of commutative semigroup rings. All these semigroup rings are containing the polynomial ring B[X; Z0]. In this paper initially we introduced the construction technique of cyclic codes through a semigroup ring B[X; 1 ak Z0] instead of a polynomial ring. After this we separately considered BCH, alternant, Goppa, Srivastava codes and by this new constructions we improve the several results of [1] by adopting the same lines as in [1].