Dual codes of product semi-linear codes

2013/06/05 by Cuitiño, Luis Felipe Tapia, Tironi, Andrea Luigi
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1306.0957

Abstract

Let \mathbbF_q be a finite field with q elements and denote by θ: \mathbbF_q→\mathbbF_q an automorphism of \mathbbF_q. In this paper, we deal with linear codes of \mathbbF_qⁿ invariant under a semi-linear map T:\mathbbF_qⁿ→\mathbbF_qⁿ for some n≥ 2. In particular, we study three kind of their dual codes, some relations between them and we focus on codes which are products of module skew codes in the non-commutative polynomial ring \mathbbF_q[X,θ] as a subcase of linear codes invariant by a semi-linear map T. In this setting we give also an algorithm for encoding, decoding and detecting errors and we show a method to construct codes invariant under a fixed T.

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