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.
Citation: |
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. | |
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. | |
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. | |
C. Carlet and S. Guilley, Complementary dual codes for counter-measures to side-channel attacks, in Proc. 4th ICMCTA Meeting, Palmela, Portugal, 2014. | |
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. | |
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. | |
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. | |
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. | |
J. L. Massey , Linear codes with complementary duals, Discrete Math., 106-107 (1992) , 337-342. doi: 10.1016/0012-365X(92)90563-U. | |
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. | |
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. |