Orateur
Patrick Solé
(Telecom ParisTech)
Description
In this article we introduce skew generalized quasi-cyclic codes over finite field $F$ with Galois automorphism $\theta$. This is a generalization of quasi-cyclic codes and skew polynomial codes.
These codes have an added advantage over quasi-cyclic codes, since the length of the code $C$ need not be a multiple of the index of $C$. After a brief description of the skew polynomial ring $F[x;\theta]$, it is shown that a skew generalized quasi-cyclic code $C$ is a left submodule of $R_1\times R_2\times \cdots R_l$, where $R_i = F[x;\theta]/(x^{m_i}-1),\,\left\vert \left\langle
\theta\right\rangle \right\vert = m$ and $m|m_{i}$ for all $i=1,\ldots ,l$. This method provides a direct construction of many codes with best known parameters over $GF(4)$.
Joint work with T. Abualrub, P. Seneviratne
