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On Linear Complementary Pairs of Codes
Date
2018-10-01
Author
CARLET, Claude
Guneri, Cem
Özbudak, Ferruh
Ozkaya, Buket
SOLE, Patrick
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Library and Information Sciences
,
Information Systems
,
Computer Science Applications
URI
https://hdl.handle.net/11511/48911
Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
DOI
https://doi.org/10.1109/tit.2018.2796125
Collections
Department of Mathematics, Article