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).

翻译：关于$q>2$的$q$元线性互补码对（LCPs）的存在性此前已得到完整刻画。本文给出了二元线性互补码对存在性的一种刻画。由此，我们解决了Carlet等人（IEEE Trans. Inf. Theory 65(3): 1694-1704, 2019）提出的一个公开问题以及Choi等人（Cryptogr. Commun. 15(2): 469-486, 2023）提出的一个猜想。