Optimal Binary Linear Complementary Pairs From Solomon-Stiffler Codes

Carlet et al. showed that for q >= 3, there exists a linear complementary pair of codes over F-q whose security parameter is as good as the minimum distance d(L) of the best linear code with the same length and dimension. For binary codes, they proved that the security parameter of a linear complementary pair of codes is lower bounded by d(L) - 1. Choi et al. recently presented infinite families of binary linear complementary pairs which are optimal in the sense that their security parameters reach d(L). Here, we prove that for every k >= 5 and d >= inverted right perpendicular(k - 1)/2inverted left perpendicular(2k-1), there exist binary linear complementary pairs of codes of length g(k, d), where g(k, d) denotes the Griesmer bound. This shows the existence of an infinite family of optimal binary LCP of codes for new code parameters, which extensively broaden those obtained by Choi et al. Our construction is explicit and it is based on codes reaching the Griesmer bound, which were constructed by Solomon and Stiffler.