An open problem and a conjecture on binary linear complementary pairs of codes

Shitao Li; Minjia Shi; San Ling

paper

An open problem and a conjecture on binary linear complementary pairs of codes

arXiv:2312.09482

Abstract

The existence of $q$ -ary linear complementary pairs (LCPs) of codes with $q > 2$ has been completely characterized so far. This paper gives a characterization for the existence of binary LCPs of codes. As a result, we solve an open problem proposed by Carlet $e t a l .$ (IEEE Trans. Inf. Theory 65(3): 1694-1704, 2019) and a conjecture proposed by Choi $e t a l .$ (Cryptogr. Commun. 15(2): 469-486, 2023).