#### Mimar Sinan Fine Arts University Mathematics Department Seminars

Concatenated Structure of q-abelian Codes and a Resulting Minimum Distance Bound
Elif Saçıkara
Sabancı University, Turkey
Özet : For a positive integer $\ell$ and a group algebra $F_q[H]$, a $q$-abelian code of index $\ell$ is a $F_q[H]$-submodule of $F_q[H]^{\ell}$, where $H$ is an abelian group of order $m$. The special case $H := Z_m$, where $Z_m$ is a cyclic group of order $m$, gives a quasi-cyclic (QC) code of index $\ell$ and length $m\ell$. So, $q$-abelian codes are natural generalization of QC codes. Sole and Ling showed that QC codes can be decomposed as a direct sum of certain linear codes of length $\ell$ by applying the Chinese Remainder Theorem, such a method is called the CRT decomposition. Jensen represented a concatenated structure of QC codes and later Guneri-Ozbudak showed that these decompositions are equivalent. In this talk, we present a concatenated structure of $q$-abelian codes by using the CRT decomposition of q-abelian codes introduced by Jitman and Ling and we show that both decompositions are equivalent. Concatenated structure also leads to asymtotical goodness and provides a general minimum distance bound, extending the analogue bound for QC codes due to Jensen. (Joint work with Cem Güneri)
 Tarih : 30.11.2017 Saat : 16:00 Yer : Seminar room, Bomonti Campus Dil : English