Jeudi 12 avril 2018 à 16h00 en salle C48
Elif Saçıkara (Sabancı University)

Titre : Concatenated Structure of Quasi-Abelian Codes and a Resulting Minimum Distance Bound

Résumé :
For a positive integer ` and a group algebra Fq[H], a quasi-abelian (QA) code of index ` is a Fq[H]-submodule of Fq[H]`, where H is an abelian group of order m. The special case H := Zm, where Zm is a cyclic group of order m, gives a quasi-cyclic (QC) code of index ` and length m`. So, QA codes are natural generalization of QC codes. Ling and Sol ́e showed that QC codes can be decomposed as a direct sum of certain linear codes of length ` by applying the Chinese Remainder Theorem, such a method is called the CRT decomposition. Jensen represented a concatenated structure of QC codes and later Güneri-Ozbudak showed that these decompositions are equivalent. In this talk, we present a concatenated structure of QA codes by using the CRT decomposition of QA 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)