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The existence of $q$-ary linear complementary pairs (LCPs) of codes with $q>2$ has been completely characterized so far. This paper gives acharacterization for the existence of binary LCPs of codes. As a result, wesolve an open problem proposed by Carlet $et~al.$ (IEEE Trans. Inf. Theory65(3): 1694-1704, 2019) and a conjecture proposed by Choi $et~al.$ (Cryptogr.Commun. 15(2): 469-486, 2023).

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