On linear complementary pair of nD cyclic codes
The security parameter for a linear complementary pair (C,D) of codes is defined to be the minimum of the minimum distances d(C) and d(D⊥). Recently, Carlet et al. showed that if C and D are both cyclic or both two-dimensional (2D) cyclic linear complementary pair of codes, then C and D⊥ are equival...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/89665 http://hdl.handle.net/10220/46715 |
| _version_ | 1826117168676208640 |
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| author | Özkaya, Buket Güneri, Cem Sayıcı, Selcen |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Özkaya, Buket Güneri, Cem Sayıcı, Selcen |
| author_sort | Özkaya, Buket |
| collection | NTU |
| description | The security parameter for a linear complementary pair (C,D) of codes is defined to be the minimum of the minimum distances d(C) and d(D⊥). Recently, Carlet et al. showed that if C and D are both cyclic or both two-dimensional (2D) cyclic linear complementary pair of codes, then C and D⊥ are equivalent codes. Hence, the security parameter for cyclic and 2D cyclic linear complementary pair of codes is simply d(C). We extend this result to nD cyclic linear complementary pair of codes. The proof of Carlet et al. for the 2D cyclic case is based on the trace representation of the codes, which is technical and nontrivial to generalize. Our proof for the generalization is based on the zero sets of the ideals corresponding to nD cyclic codes. |
| first_indexed | 2024-10-01T04:23:15Z |
| format | Journal Article |
| id | ntu-10356/89665 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:23:15Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/896652023-02-28T19:29:58Z On linear complementary pair of nD cyclic codes Özkaya, Buket Güneri, Cem Sayıcı, Selcen School of Physical and Mathematical Sciences LCP Of Codes nD Cyclic Codes DRNTU::Science::Mathematics The security parameter for a linear complementary pair (C,D) of codes is defined to be the minimum of the minimum distances d(C) and d(D⊥). Recently, Carlet et al. showed that if C and D are both cyclic or both two-dimensional (2D) cyclic linear complementary pair of codes, then C and D⊥ are equivalent codes. Hence, the security parameter for cyclic and 2D cyclic linear complementary pair of codes is simply d(C). We extend this result to nD cyclic linear complementary pair of codes. The proof of Carlet et al. for the 2D cyclic case is based on the trace representation of the codes, which is technical and nontrivial to generalize. Our proof for the generalization is based on the zero sets of the ideals corresponding to nD cyclic codes. Accepted version 2018-11-27T07:49:53Z 2019-12-06T17:30:42Z 2018-11-27T07:49:53Z 2019-12-06T17:30:42Z 2018 2018 Journal Article Güneri, C., Özkaya, B., & Sayıcı , S. On linear complementary pair of nD cyclic codes. IEEE Communications Letters, 1-1. doi:10.1109/LCOMM.2018.2872046 1089-7798 https://hdl.handle.net/10356/89665 http://hdl.handle.net/10220/46715 10.1109/LCOMM.2018.2872046 208996 en IEEE Communications Letters © 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: [http://dx.doi.org/10.1109/LCOMM.2018.2872046]. 4 p. application/pdf |
| spellingShingle | LCP Of Codes nD Cyclic Codes DRNTU::Science::Mathematics Özkaya, Buket Güneri, Cem Sayıcı, Selcen On linear complementary pair of nD cyclic codes |
| title | On linear complementary pair of nD cyclic codes |
| title_full | On linear complementary pair of nD cyclic codes |
| title_fullStr | On linear complementary pair of nD cyclic codes |
| title_full_unstemmed | On linear complementary pair of nD cyclic codes |
| title_short | On linear complementary pair of nD cyclic codes |
| title_sort | on linear complementary pair of nd cyclic codes |
| topic | LCP Of Codes nD Cyclic Codes DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/89665 http://hdl.handle.net/10220/46715 |
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