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arXiv · 1304.6518

(Sigma-Delta) Codes

M. Boulagouaz·A. Leroy
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Abstract

In this paper we introduce the notion of cyclic ($f(t),σ,δ$)-codes for $f(t)\in \Ore$. These codes generalize the $θ$-codes as introduced by D. Boucher, F. Ulmer, W. Geiselmann \cite{BGU}. We construct generic and control matrices for these codes. As a particular case the ($\si,\de$)-$W$-code associated to a Wedderburn polynomial are defined and we show that their control matrices are given by generalized Vandermonde matrices. All the Wedderburn polynomials of $\mathbb F_q[t;θ]$ are described and their control matrices are presented. A key role will be played by the pseudo-linear transformations.

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M. Boulagouaz, A. Leroy. 2013-04-24. (Sigma-Delta) Codes. https://arxiv.org/abs/1304.6518

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