On Linear Complementary Pairs of Codes
| Autor: | Buket Özkaya, Ferruh Özbudak, Claude Carlet, Patrick Solé, Cem Güneri |
|---|---|
| Přispěvatelé: | School of Physical and Mathematical Sciences |
| Rok vydání: | 2018 |
| Předmět: |
Linear programming
Binary number Data_CODINGANDINFORMATIONTHEORY 0102 computer and information sciences 02 engineering and technology Library and Information Sciences Characterization (mathematics) 01 natural sciences 0202 electrical engineering electronic engineering information engineering Code (cryptography) Algebraic number Computer Science::Data Structures and Algorithms Circulant matrix Discrete mathematics QA075 Electronic computers. Computer science Quasi-cyclic Code 020206 networking & telecommunications Special class Quantitative Biology::Genomics Computer Science Applications 010201 computation theory & mathematics QA150-272.5 Algebra Electrical and electronic engineering [Engineering] Constacyclic Code Security parameter Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 64:6583-6589 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2018.2796125 |
| Popis: | 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 quasi-cyclic 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^\bot $ are equivalent to each other. Hence, the security parameter $\min (d(C),d(D^\bot))$ 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 $d(C)=d(D^\bot)$ . This extends the linear programming bound for LCD codes. |
| Databáze: | OpenAIRE |
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