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On construction of bent functions involving symmetric functions and their duals
On complementary dual additive cyclic codes
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 |
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.
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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[9] |
J. L. Massey,
Linear codes with complementary duals, Discrete Math., 106-107 (1992), 337-342.
doi: 10.1016/0012-365X(92)90563-U. |
[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. |
[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. |
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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[9] |
J. L. Massey,
Linear codes with complementary duals, Discrete Math., 106-107 (1992), 337-342.
doi: 10.1016/0012-365X(92)90563-U. |
[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. |
[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. |
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