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Article Dans Une Revue Lecture Notes in Computer Science Année : 2009

Codes as modules over skew polynomial rings

Résumé

In previous works we considered codes dened as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes dened as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes dened as ideals. The notion of BCH codes can be extended to this new approach and the codes whose duals are also dened as modules can be characterized. We show that under some restriction, self dual module codes must be constacyclic ideal codes and found two non equivalent Euclidean self-dual [56; 28; 15]4 codes which improve the best previously known distance 14 for self-dual codes of this length over F4.
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Dates et versions

hal-00398355 , version 1 (24-06-2009)

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  • HAL Id : hal-00398355 , version 1

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Delphine Boucher, Félix Ulmer. Codes as modules over skew polynomial rings. Lecture Notes in Computer Science, 2009, 5921, pp.38-55. ⟨hal-00398355⟩
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