An open problem and a conjecture on binary linear complementary pairs of codes
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 et~al. (IEEE Trans. Inf. Theory 65(3): 1694-1704, 2019) and a conjecture proposed by Choi et~al. (Cryptogr. Commun. 15(2): 469-486, 2023).
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