Explicit construction of optimal binary linear complementary pairs via Belov codes

Abstract

The study of linear complementary pairs (LCPs) has been a hot topic in coding theory. Recently, Güneri constructed an infinite family of optimal binary LCPs from Solomon-Stiffler codes. Specifically, he proved that for every $k\ge 5$ and $d\ge \lceil (k-1)/2\rceil 2^{k-1}$, there exist optimal binary linear complementary pairs of codes of length $g_2(k,d)$, where $g_2(k,d)$ denotes the Griesmer bound. In this paper, we construct additional optimal binary LCPs from Belov codes, which form a generalized class of Solomon-Stiffler codes. Our results not only generalize Güneri's construction, but also enable more flexible construction of optimal binary LCPs with a wide range of minimum distances.

arXiv comment30 pages