ON ADDITIVE CYCLIC CODES

Funda Özdemir
Mathematics, PhD Dissertation, 2016

Thesis Jury

Assoc. Prof. Dr. Cem Güneri (Thesis Advisor),  Prof. Dr. Henning Stichtenoth,  Prof. Dr. Albert Levi,  Asst. Prof. Dr. Burcu Gülmez Temür,  Asst. Prof. Dr. Seher Tutdere

Date & Time: August 4th, 2016 –  2:00 PM

Place:  FENS 2008

Keywords : Additive cyclic code, algebraic curve over a finite field, Hasse-Weil bound, BCH bound, complementary dual code.

Abstract

In this thesis we consider two problems related to additive cyclic codes. In the first part, we obtain a lower bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound for classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer's BCH bound. We compare our bound's performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results. In the second part, we study complementary dual additive cyclic codes. We give a sufficient condition for a special class of additive cyclic codes to be complementary dual.