PreprintCC BY-NC-SA 4.0arXiv
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 ≥ 5 and d ≥ ⌈ (k − 1)/2 ⌉ 2k − 1, there exist optimal binary linear complementary pairs of codes of length g2(k,d), where g2(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.
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BibTeX
@misc{wu2026explicit,
title = {{Explicit construction of optimal binary linear complementary pairs via Belov codes}},
author = {Yansheng Wu and Jing Chen and Jong Yoon Hyun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24019},
eprint = {2610.24019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24019},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Explicit construction of optimal binary linear complementary pairs via Belov codes
AU - Yansheng Wu
AU - Jing Chen
AU - Jong Yoon Hyun
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24019
UR - https://arxiv.org/abs/2610.24019
AB - 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 ≥ 5 and d ≥ ⌈ (k − 1)/2 ⌉ 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.
ER -