Abstract
A concatenated construction for linear complementary dual codes was given by Carlet et al. using the so-called isometry inner codes. Here, we obtain a concatenated construction to the more general family, linear complementary pair of codes. Moreover, we extend the dual code description of Chen et al. for concatenated codes to duals of generalized concatenated codes. This allows us to use generalized concatenated codes for the construction of linear complementary pair of codes.
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Bhasin, S., Danger, J.-L., Guilley, S., Najm, Z., Ngo, X.T.: Linear complementary dual code improvement to strengthen encoded circuit against hardware Trojan horses, IEEE International Symposium on Hardware Oriented Security and Trust (HOST), May 5–7 (2015)
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: The user language. J. Symbol. Comput. 24, 235–265 (1997)
Bringer, J., Carlet, C., Chabanne, H., Guilley, S., Maghrebi, H.: Orthogonal direct sum masking - a smartcard friendly computation paradigm in a code with builtin protection against side-channel and fault attacks. In: WISTP, pp 40–56. Springer, Heraklion (2014)
Carlet, C., Guilley, S.: Complementary dual codes for counter-measures to side-channel attacks, Adv. Math. Commun. 10, 131–150 (2016)
Carlet, C., Mesnager, S., Tang, C., Qi, Y.: Euclidean and Hermitian LCD MDS codes, Des., Codes. Cryptogr. 86, 2605–2618 (2018)
Carlet, C., Mesnager, S., Tang, C., Qi, Y., Pellikaan, R.: Linear codes over \(\mathbb {F}_{q}\) are equivalent to LCD codes for q > 3. IEEE Trans. Inform. Theory 64, 3010–3017 (2018)
Carlet, C., Güneri, C., Özbudak, F., Özkaya, B., Solé, P.: On linear complementary pairs of codes. IEEE Trans. Inform. Theory 64, 6583–6589 (2018)
Carlet, C., Güneri, C., Özbudak, F., Solé, P.: A new concatenated type construction for LCD codes and isometry codes. Discrete Math. 341, 830–835 (2018)
Chen, H., Ling, S., Xing, C.: Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound. IEEE Trans. Inform. Theory 47, 2055–2058 (2001)
Cordaro, J.T., Wagner, T.: Optimum (n, 2) codes for small values of channel error probability. PGIT 13, 349–350 (1967)
Dumer, I.: Concatenated codes and their multilevel generalizations, pp 1911–1988. Handbook of Coding Theory, North-Holland (1998)
Dougherty, S.T., Kim, J. -L., Özkaya, B., Sok, L., Solé, P.: The combinatorics of LCD codes: Linear programming bound and orthogonal matrices. Int. J. Inform. Coding Theory 4(2/3), 116–128 (2017)
Güneri, C., Özkaya, B., Solé, P.: Quasi-cyclic complementary dual codes. Finite Fields Appl. 42, 67–80 (2016)
Li, C., Ding, C., Li, S.: LCD cyclic codes over finite fields. IEEE Trans. Inform. Theory 63, 4344–4356 (2017)
Mesnager, S., Tang, C., Qi, Y.: Complementary dual algebraic geometry codes. IEEE Trans. Inform. Theory 64, 2390–2397 (2018)
Sendrier, N.: Linear codes with complementary duals meet the Gilbert-Varshamov bound. Discrete Math. 285, 345–347 (2004)
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The authors are supported by TÜBİTAK project 215E200, which is associated with the SECODE project in the scope of CHIST-ERA Program.
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Güneri, C., Özbudak, F. & Saçıkara, E. A concatenated construction of linear complementary pair of codes. Cryptogr. Commun. 11, 1103–1114 (2019). https://doi.org/10.1007/s12095-019-0354-5
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DOI: https://doi.org/10.1007/s12095-019-0354-5