On linear complementary pairs of codes

Carlet, Claude and Güneri, Cem and Özbudak, Ferruh and Özkaya, Buket and Sole, Patrick (2018) On linear complementary pairs of codes. IEEE Transactions on Information Theory, 64 (10). pp. 6583-6589. ISSN 0018-9448 (Print) 1557-9654 (Online)

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We study linear complementary pairs (LCP) of codes (C, D), where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasicyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes. Our result for the constacyclic complementary pairs extends the characterization of linear complementary dual (LCD) cyclic codes given by Yang and Massey. We observe that when C and I) are complementary and constacyclic, the codes C and D-perpendicular to are equivalent to each other. Hence, the security parameter min(d(C), d(D-perpendicular to)) for LCP of codes is simply determined by one of the codes in this case. The same holds for a special class of quasi-cyclic codes, namely 2D cyclic codes, but not in general for all quasi-cyclic codes, since we have examples of LCP of double circulant codes not satisfying this conclusion for the security parameter. We present examples of binary LCP of quasi-cyclic codes and obtain several codes with better parameters than known binary LCD codes. Finally, a linear programming hound is obtained for binary LCP of codes and a table of values from this bound is presented in the case d(C) = d(D-perpendicular to). This extends the linear programming bound for LCD codes.
Item Type: Article
Uncontrolled Keywords: Constacyclic code; quasi-cyclic code; LCP of codes; linear programming bound
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Q Science > QA Mathematics > QA075 Electronic computers. Computer science
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 03 Aug 2019 16:16
Last Modified: 22 May 2023 14:06
URI: https://research.sabanciuniv.edu/id/eprint/39013

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