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May  2017, 11(2): 353-357. doi: 10.3934/amc.2017028

On complementary dual additive cyclic codes

Cem Güneri 1, , Ferruh Özbudak 2, and  Funda ÖzdemIr 1,

1. 

Faculty of Engineering and Natural Sciences, Sabancı University, 34956, İstanbul, Turkey
2. 

Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey

Received  February 2016 Revised  March 2016 Published  May 2017

A code is said to be complementary dual if it meets its dual trivially. We give a sufficient condition for a special class of additive cyclic codes to be complementary dual.

Keywords: Additive cyclic code, complementary dual code.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Cem Güneri, Ferruh Özbudak, Funda ÖzdemIr. On complementary dual additive cyclic codes. Advances in Mathematics of Communications, 2017, 11 (2) : 353-357. doi: 10.3934/amc.2017028
References:
[1]

J. Bierbrauer, The theory of cyclic codes and a generalization to additive codes, Des. Codes Crypt., 25 (2002), 189-206. doi: 10.1023/A:1013808515797. Google Scholar

[2]

J. Bierbrauer and Y. Edel, Quantum twisted codes, J. Combin. Des., 8 (2000), 174-188. doi: 10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T. Google Scholar

[3]

W. Bosma, J. Cannon and C. Playoust, The Magma algebra system Ⅰ. The user language, J. Symb. Comput., 24 (1997), 235-265. doi: 10.1006/jsco.1996.0125. Google Scholar

[4]

C. Carlet and S. Guilley, Complementary dual codes for counter-measures to side-channel attacks, in Proc. 4th ICMCTA Meeting, Palmela, Portugal, 2014.Google Scholar

[5]

M. Esmaeili and S. Yari, On complementary-dual quasi-cyclic codes, Finite Fields Appl., 15 (2009), 375-386. doi: 10.1016/j.ffa.2009.01.002. Google Scholar

[6]

C. Güneri, Artin-Schreier curves and weights of two-dimensional cyclic codes, Finite Fields Appl., 10 (2004), 481-505. doi: 10.1016/j.ffa.2003.10.002. Google Scholar

[7]

C. Güneri, F. Özbudak and F. Özdemir, Hasse-Weil bound for additive cyclic codes, Des. Codes Crypt., 82 (2017), 249-263. doi: 10.1007/s10623-016-0198-3. Google Scholar

[8]

C. Güneri, B. Özkaya and P. Solé, Quasi-cyclic complementary dual codes, Finite Fields Appl., 42 (2016), 67-80. doi: 10.1016/j.ffa.2016.07.005. Google Scholar

[9]

J. L. Massey, Linear codes with complementary duals, Discrete Math., 106-107 (1992), 337-342. doi: 10.1016/0012-365X(92)90563-U. Google Scholar

[10]

N. Sendrier, Linear codes with complementary duals meet the Gilbert-Varshamov bound, Discrete Math., 285 (2004), 345-347. doi: 10.1016/j.disc.2004.05.005. Google Scholar

[11]

X. Yang and J. L. Massey, The condition for a cyclic code to have a complementary dual, Discrete Math., 126 (1994), 391-393. doi: 10.1016/0012-365X(94)90283-6. Google Scholar

show all references

References:
[1]

J. Bierbrauer, The theory of cyclic codes and a generalization to additive codes, Des. Codes Crypt., 25 (2002), 189-206. doi: 10.1023/A:1013808515797. Google Scholar

[2]

J. Bierbrauer and Y. Edel, Quantum twisted codes, J. Combin. Des., 8 (2000), 174-188. doi: 10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO;2-T. Google Scholar

[3]

W. Bosma, J. Cannon and C. Playoust, The Magma algebra system Ⅰ. The user language, J. Symb. Comput., 24 (1997), 235-265. doi: 10.1006/jsco.1996.0125. Google Scholar

[4]

C. Carlet and S. Guilley, Complementary dual codes for counter-measures to side-channel attacks, in Proc. 4th ICMCTA Meeting, Palmela, Portugal, 2014.Google Scholar

[5]

M. Esmaeili and S. Yari, On complementary-dual quasi-cyclic codes, Finite Fields Appl., 15 (2009), 375-386. doi: 10.1016/j.ffa.2009.01.002. Google Scholar

[6]

C. Güneri, Artin-Schreier curves and weights of two-dimensional cyclic codes, Finite Fields Appl., 10 (2004), 481-505. doi: 10.1016/j.ffa.2003.10.002. Google Scholar

[7]

C. Güneri, F. Özbudak and F. Özdemir, Hasse-Weil bound for additive cyclic codes, Des. Codes Crypt., 82 (2017), 249-263. doi: 10.1007/s10623-016-0198-3. Google Scholar

[8]

C. Güneri, B. Özkaya and P. Solé, Quasi-cyclic complementary dual codes, Finite Fields Appl., 42 (2016), 67-80. doi: 10.1016/j.ffa.2016.07.005. Google Scholar

[9]

J. L. Massey, Linear codes with complementary duals, Discrete Math., 106-107 (1992), 337-342. doi: 10.1016/0012-365X(92)90563-U. Google Scholar

[10]

N. Sendrier, Linear codes with complementary duals meet the Gilbert-Varshamov bound, Discrete Math., 285 (2004), 345-347. doi: 10.1016/j.disc.2004.05.005. Google Scholar

[11]

X. Yang and J. L. Massey, The condition for a cyclic code to have a complementary dual, Discrete Math., 126 (1994), 391-393. doi: 10.1016/0012-365X(94)90283-6. Google Scholar

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