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# Number theory days

23-27 juin 2014
Université Lille 1
Europe/Paris timezone
Accueil > Timetable > Session details > Contribution details

# Contribution

Université Lille 1 - Salle de réunions
Noncommutative algebra

# Skew Generalized Quasi-Cyclic Codes

• Patrick SOLÉ

## 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