ON LINEAR COMPLEMENTARY PAIR OF CODES

Selcen Sayıcı
Mathematics, PhD Dissertation, 2020

Thesis Jury

Prof. Cem Güneri, Prof. Erkay Savaş, Assoc. Prof. Kağan Kurşungöz,

Prof. Ferruh Özbudak, Assoc. Prof. Alp Bassa

Date & Time: July 23rd, 2020  –  13:30 PM

Place: Zoom Meeting

https://zoom.us/j/2334047777

Keywords : Linear complementary pair of codes, abelian codes, group codes, code equivalence, finite fields, finite chain rings

Abstract

Linear complementary pair (C, D) of codes has drawn much attention recently due to their applications to cryptography, in the context of side channel and fault injection attacks. The security parameter of such a pair is defined to be the minimum of the minimum distances d(C) and d(D^\bot). Carlet et al. showed that if C and D are both cyclic or both 2D cyclic over a finite field, then C and D^\bot are equivalent codes. Hence d(C) = d(D^\bot). We extend this result to all nD cyclic, or abelian, codes over finite fields. Moreover, we prove the same result for all linear complementary pair of 2-sided group codes over finite chain rings.