Abstract
<abstract><p>Linear codes with complementary-duals (LCD codes) are linear codes that trivially intersect with their dual (Massey, 1992). In this paper, we study double circulant codes (DC codes), which are a special class of quasi-cyclic codes, over $ \mathbb{F}_4 $ that are LCD. The main techniques used are as follows: Chinese reminder theory (CRT) decomposition in the line of (Ling et al. 2001), explicit enumeration, and asymptotics. In particular, we show that the class of codes considered here is asymptotically good.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference13 articles.
1. C. Carlet, S. Mesnager, C. Tang, Y. Qi, R. Pellikaan, Linear codes over $ \mathbb{F}_q$ are equivalent to LCD codes for $q>3$, IEEE Trans. Inf. Theory, 64 (2018), 3010–3017. https://doi.org/10.1109/TIT.2018.2789347
2. C. Carlet, S. Guilley, Coding theory and applications, Springer, 2015. https://doi.org/10.1007/978-3-319-17296-5-9
3. S. T. Dougherty, J. L. Kim, B. Ozkaya, L. Sok, P. Solé, The combinatorics of LCD codes: linear programming bound and orthogonal matrices, Int. J. Inf. Coding Theory, 4 (2017), 116–128. https://doi.org/10.1504/IJICOT.2017.083827
4. Bounds on the minimum distance of linear codes and quantum codes, Markus Grassl, 2023. Available from: http://www.codetables.de.
5. C. Güneri, B. Özkaya, P. Solé, Quasi-cyclic complementary dual codes, Finite Fields Appl., 42 (2016), 67–80. https://doi.org/10.1016/j.ffa.2016.07.005