Sabancı University Algebra Seminars

On Abelian LCP of Codes over Chain Rings.
Selcen Sayıcı
Sabancı University, Turkey
Özet : Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side channel and fault injection attacks. If $C$ and $D$ are linear codes of length $n$ over $F_q$ , the pair $(C, D)$ is said to be an LCP of codes if $C\oplus D=F^n_q$. In the special case $C=D^\bot$, the code $C$ is called an LCD code. The security parameter for an LCP of codes $(C, D)$ is defined as the minimum of the minimum distances $d(C)$ and $d(D^\bot)$. It has recently been shown that if $C$ and $D$ are both cyclic or both 2D cyclic LCP of codes over a finite field $F_q$, then $C$ and $D^\bot$ are equivalent , and hence the security parameter for the pair $(C, D)$ is simply $d(C)$. In this talk, we first generalize this result to abelian ($nD$ cyclic) LCP of codes over finite fields when the length of the codes is relatively prime to the characteristic of the field. Then we focus on further extensions of this result. We remove the restriction on the code length in the case of abelian LCP’s over finite fields. Moreover, we prove the same fact for an LCP of abelian codes over any finite chain ring. This is joint work with Cem Güneri and Edgar Martinez-Moro.
  Tarih : 12.02.2020
  Saat : 12:40
  Yer : FENS building on Sabancı Campus in room G035.
  Dil : English