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Sociedade Brasileira de Telecomunicações

Ascending chains of monoid and encoding


Let B be any fixed finite commutative ring with identity and k ≥ 0 is an integer. For any prime p there are the ascending chains B[X; Z0] ⊂ B[X; 1 p Z0] ⊂ B[X; 21p Z0] ⊂ · · · ⊂ B[X; kp 1 Z0] ⊂ · · · of commutative monoid rings, where Z0 ⊂ 1 p Z0 ⊂ 21p Z0 ⊂ · · · ⊂ kp 1 Z0 ⊂ · · · are the ascending chains of cyclic monoids. We established the construction technique of cyclic codes through the monoid ring B[X; kp 1 Z0] instead of a polynomial ring. Moreover we independently considered BCH, alternant, Goppa, Srivastava codes through a monoid ring B[X; kp 1 Z0], where we improved several results of [1] in more broader sense

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