On linear complementary pairs of codes
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 consta...
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| Format: | Journal Article |
| Language: | English |
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2019
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| Online Access: | https://hdl.handle.net/10356/88810 http://hdl.handle.net/10220/49111 |
| _version_ | 1824454150002311168 |
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| author | Solé, Patrick Carlet, Claude Güneri, Cem Özbudak, Ferruh Özkaya, Buket |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Solé, Patrick Carlet, Claude Güneri, Cem Özbudak, Ferruh Özkaya, Buket |
| author_sort | Solé, Patrick |
| collection | NTU |
| description | 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. |
| first_indexed | 2025-02-19T03:17:44Z |
| format | Journal Article |
| id | ntu-10356/88810 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:17:44Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/888102023-02-28T19:36:12Z On linear complementary pairs of codes Solé, Patrick Carlet, Claude Güneri, Cem Özbudak, Ferruh Özkaya, Buket School of Physical and Mathematical Sciences Engineering::Electrical and electronic engineering Constacyclic Code Quasi-cyclic Code 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. Accepted version 2019-07-03T06:52:06Z 2019-12-06T17:11:20Z 2019-07-03T06:52:06Z 2019-12-06T17:11:20Z 2018 2018 Journal Article 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 0018-9448 https://hdl.handle.net/10356/88810 http://hdl.handle.net/10220/49111 10.1109/TIT.2018.2796125 206928 en IEEE Transactions on Information Theory © 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: https://doi.org/10.1109/TIT.2018.2796125 application/pdf |
| spellingShingle | Engineering::Electrical and electronic engineering Constacyclic Code Quasi-cyclic Code Solé, Patrick Carlet, Claude Güneri, Cem Özbudak, Ferruh Özkaya, Buket On linear complementary pairs of codes |
| title | On linear complementary pairs of codes |
| title_full | On linear complementary pairs of codes |
| title_fullStr | On linear complementary pairs of codes |
| title_full_unstemmed | On linear complementary pairs of codes |
| title_short | On linear complementary pairs of codes |
| title_sort | on linear complementary pairs of codes |
| topic | Engineering::Electrical and electronic engineering Constacyclic Code Quasi-cyclic Code |
| url | https://hdl.handle.net/10356/88810 http://hdl.handle.net/10220/49111 |
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