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Factorisation in M'(Fq)[X]. Construction of quasi-cyclic codes

Christophe Chabot 1 
Abstract : Quasi-cyclic codes are viewed as codes cancelled by polynomials with matricial coefficients. This construction leads to the problem of factorisation of Xm -1 in M'(Fq)[X]. In this paper we deal with the general factorisation in M'(Fq)[X]. Then we give results on the roots and the factorisation of the particular polynomial Xm -1. These factorisations permit the construction of such quasi-cyclic codes. We show that in most cases, these codes meet best known bounds for minimum distances. We even found two new codes with parameters better than known [30; 22; 6]F4 and [29; 21; 6]F4 .
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Submitted on : Wednesday, July 27, 2011 - 2:30:53 PM
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  • HAL Id : inria-00611781, version 1

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Christophe Chabot. Factorisation in M'(Fq)[X]. Construction of quasi-cyclic codes. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.209-218. ⟨inria-00611781⟩

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