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Title: On linear complementary pairs of codes
Authors: Solé, Patrick
Carlet, Claude
Güneri, Cem
Özbudak, Ferruh
Özkaya, Buket
Keywords: Engineering::Electrical and electronic engineering
Constacyclic Code
Quasi-cyclic Code
Issue Date: 2018
Source: Carlet, C., Güneri, C., Özbudak, F., Özkaya, B., & Solé, P. (2018). On linear complementary pairs of codes. IEEE Transactions on Information Theory, 64(10), 6583-6589. doi:10.1109/TIT.2018.2796125
Series/Report no.: IEEE Transactions on Information Theory
Abstract: 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 D are complementary and constacyclic, the codes C and D⊥ are equivalent to each other. Hence, the security parameter min(d(C), d(D⊥)) 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 bound is obtained for binary LCP of codes and a table of values from this bound is presented in the case d(C) = d(D⊥). This extends the linear programming bound for LCD codes.
ISSN: 0018-9448
DOI: 10.1109/TIT.2018.2796125
Rights: © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
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