The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Applicable Algebra in Engineering, Communication and Computing
Skew codes of prescribed distance or rank
Designs, Codes and Cryptography
Coding with skew polynomial rings
Journal of Symbolic Computation
Skew quasi-cyclic codes over Galois rings
Designs, Codes and Cryptography
A note on the dual codes of module skew codes
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Self-dual skew codes and factorization of skew polynomials
Journal of Symbolic Computation
Linear codes using skew polynomials with automorphisms and derivations
Designs, Codes and Cryptography
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In previous works we considered codes defined as ideals of quotients of skew polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over skew polynomial rings, removing therefore some of the constraints on the length of the skew codes defined as ideals. The notion of BCH codes can be extended to this new approach and the skew codes whose duals are also defined as modules can be characterized. We conjecture that self-dual skew codes defined as modules must be constacyclic and prove this conjecture for the Hermitian scalar product and under some assumptions for the Euclidean scalar product. We found new [56, 28, 15], [60,30,16], [62,31,17], [66,33,17] Euclidean self-dual skew codes and new [50,25,14], [58,29,16] Hermitian self-dual skew codes over F 4 , improving the best known distances for self-dual codes of these lengths over F 4 .