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...

Full description

Saved in:
Bibliographic Details
Main Authors: Özkaya, Buket, Güneri, Cem, Sayıcı, Selcen
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2018
Subjects:
Online Access:https://hdl.handle.net/10356/89665
http://hdl.handle.net/10220/46715
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-89665
record_format dspace
spelling sg-ntu-dr.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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic LCP Of Codes
nD Cyclic Codes
DRNTU::Science::Mathematics
spellingShingle LCP Of Codes
nD Cyclic Codes
DRNTU::Science::Mathematics
Özkaya, Buket
Güneri, Cem
Sayıcı, Selcen
On linear complementary pair of nD cyclic codes
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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Özkaya, Buket
Güneri, Cem
Sayıcı, Selcen
format Article
author Özkaya, Buket
Güneri, Cem
Sayıcı, Selcen
author_sort Özkaya, Buket
title On linear complementary pair of nD cyclic codes
title_short 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_sort on linear complementary pair of nd cyclic codes
publishDate 2018
url https://hdl.handle.net/10356/89665
http://hdl.handle.net/10220/46715
_version_ 1759854717765156864