American Institute of Mathematical Sciences

Advanced
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

[1]

Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45
[2]

Masaaki Harada, Takuji Nishimura. An extremal singly even self-dual code of length 88. Advances in Mathematics of Communications, 2007, 1 (2) : 261-267. doi: 10.3934/amc.2007.1.261
[3]

Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1
[4]

Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003
[5]

M. De Boeck, P. Vandendriessche. On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$. Advances in Mathematics of Communications, 2014, 8 (3) : 281-296. doi: 10.3934/amc.2014.8.281
[6]

Sihuang Hu, Gabriele Nebe. There is no $[24,12,9]$ doubly-even self-dual code over $\mathbb F_4$. Advances in Mathematics of Communications, 2016, 10 (3) : 583-588. doi: 10.3934/amc.2016027
[7]

Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032
[8]

Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399
[9]

Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889
[10]

Martino Borello, Francesca Dalla Volta, Gabriele Nebe. The automorphism group of a self-dual $[72,36,16]$ code does not contain $\mathcal S_3$, $\mathcal A_4$ or $D_8$. Advances in Mathematics of Communications, 2013, 7 (4) : 503-510. doi: 10.3934/amc.2013.7.503
[11]

M. Delgado Pineda, E. A. Galperin, P. Jiménez Guerra. MAPLE code of the cubic algorithm for multiobjective optimization with box constraints. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 407-424. doi: 10.3934/naco.2013.3.407
[12]

Andrew Klapper, Andrew Mertz. The two covering radius of the two error correcting BCH code. Advances in Mathematics of Communications, 2009, 3 (1) : 83-95. doi: 10.3934/amc.2009.3.83
[13]

José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Information--bit error rate and false positives in an MDS code. Advances in Mathematics of Communications, 2015, 9 (2) : 149-168. doi: 10.3934/amc.2015.9.149
[14]

Claude Carlet, Sylvain Guilley. Complementary dual codes for counter-measures to side-channel attacks. Advances in Mathematics of Communications, 2016, 10 (1) : 131-150. doi: 10.3934/amc.2016.10.131
[15]

Lisha Wang, Huaming Song, Ding Zhang, Hui Yang. Pricing decisions for complementary products in a fuzzy dual-channel supply chain. Journal of Industrial & Management Optimization, 2019, 15 (1) : 343-364. doi: 10.3934/jimo.2018046
[16]

Michael Kiermaier, Johannes Zwanzger. A $\mathbb Z$4-linear code of high minimum Lee distance derived from a hyperoval. Advances in Mathematics of Communications, 2011, 5 (2) : 275-286. doi: 10.3934/amc.2011.5.275
[17]

Anna-Lena Horlemann-Trautmann, Kyle Marshall. New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions. Advances in Mathematics of Communications, 2017, 11 (3) : 533-548. doi: 10.3934/amc.2017042
[18]

Denis S. Krotov, Patric R. J.  Östergård, Olli Pottonen. Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code. Advances in Mathematics of Communications, 2016, 10 (2) : 393-399. doi: 10.3934/amc.2016013
[19]

Jianying Fang. 5-SEEDs from the lifted Golay code of length 24 over Z4. Advances in Mathematics of Communications, 2017, 11 (1) : 259-266. doi: 10.3934/amc.2017017
[20]

W. Cary Huffman. Additive cyclic codes over $\mathbb F_4$. Advances in Mathematics of Communications, 2008, 2 (3) : 309-343. doi: 10.3934/amc.2008.2.309

2018 Impact Factor: 0.879

Tools

Metrics

  • PDF downloads (11)
  • HTML views (3)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences