Optimal binary linear complementary pairs of codes

Choi, Whan Hyuk and Güneri, Cem and Kim, Jon Lark and Özbudak, Ferruh (2023) Optimal binary linear complementary pairs of codes. Cryptography and Communications, 15 (2). pp. 469-486. ISSN 1936-2447 (Print) 1936-2455 (Online)

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A pair of linear codes (C, D) of length n over Fq is called a linear complementary pair (LCP) if their direct sum yields the full space Fqn. By a result of Carlet et al. (2019), the best security parameters of binary LCPs of codes are left open. Motivated by this, we study binary LCPs of codes. We describe a sufficient condition for binary LCPs of codes which are not optimal. We carry out an exhaustive search to determine the best security parameters for binary LCPs of codes up to length 18. We also obtain results on optimal binary LCPs of codes for infinitely many parameters. For any k≥ 2 and length n congruent to 0 or 1 mod (2 k- 1) , we prove that binary [n, k] LCPs of codes are optimal. Binary LCPs of codes of dimensions 2, 3, and 4 are also optimal for all lengths except for two instances, when (n, k) = (4 , 3) and (8, 4). We provide explicit constructions of these infinite families of optimal LCPs. Our results also indicate that many security parameters coming from binary LCPs of codes exceed those from binary LCD codes by 1 or 2.
Item Type: Article
Uncontrolled Keywords: Griesmer bound; Linear complementary pair; Optimal code; Simplex code
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 27 Mar 2023 16:25
Last Modified: 27 Mar 2023 16:25
URI: https://research.sabanciuniv.edu/id/eprint/45159

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