Self-dual skew codes and factorization of skew polynomials
نویسندگان
چکیده
منابع مشابه
Self-dual skew codes and factorization of skew polynomials
The construction of cyclic codes can be generalized to so-called ”module θ-codes” using noncommutative polynomials. The product of the generator polynomial g of a self-dual ”module θ-code” and its ”skew reciprocal polynomial” is known to be a noncommutative polynomial of the form X − a, reducing the problem of the computation of all such codes to the resolution of a polynomial system where the ...
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The aim of this text is to construct and to enumerate self-dual θ-cyclic and θ-negacyclic codes over IFp2 where p is a prime number and θ is the Frobenius automorphism.
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In [4], starting from an automorphism θ of a finite field Fq and a skew polynomial ring R = Fq[X; θ], module θ-codes are defined as left R-submodules of R/Rf where f ∈ R. In [4] it is conjectured that an Euclidean self-dual module θ-code is a θ-constacyclic code and a proof is given in the special case when the order of θ divides the length of the code. In this paper we prove that this conjectu...
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In this work the definition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings, whose multiplication is defined using an automorphism and a derivation. This produces a more general class of codes which, in some cases, produce better distance bounds than module skew codes constructed only with an automorphism. Extending the approach of Gab...
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[l] T.A. Gulliver and V.K. Bhargava, “Some best rate l / p and rate (p l ) / p systematic quasi-cyclic codes,” IEEE Trans. Inform. Theory, vol. IT-37, pp. 552-555, May 1991. [2] T.A. Gulliver and V.K. Bhargava, “Nine good rate (m l) /pm quasicyclic codes,” IEEE Trans. Inform. Theory, vol. IT-38, pp. 1366-1369, July 1992. [3] G.E. S6guin and G. Drolet, “The theory of 1-generator quasi-cyclic cod...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2014
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2013.10.003