# American Institute of Mathematical Sciences

November  2013, 7(4): 463-474. doi: 10.3934/amc.2013.7.463

## ($\sigma,\delta$)-codes

 1 University of King Khalid, Abha, Saudi Arabia 2 Université d'Artois, Lille Nord de France, Rue Jean Souvraz, Lens, 62300, France

Received  October 2012 Published  October 2013

In this paper we introduce the notion of cyclic ($f(t),\sigma,\delta$)-codes for $f(t)\in A[t;\sigma,\delta]$. These codes generalize the $\theta$-codes as introduced by D. Boucher, F. Ulmer, W. Geiselmann [2]. We construct generic and control matrices for these codes. As a particular case the ($\sigma,\delta$)-$W$-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 $\mathbb F_q[t;\theta]$ are described and their control matrices are presented. A key role will be played by the pseudo-linear transformations.
Citation: M'Hammed Boulagouaz, André Leroy. ($\sigma,\delta$)-codes. Advances in Mathematics of Communications, 2013, 7 (4) : 463-474. doi: 10.3934/amc.2013.7.463
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