As a branch of applied mathematics, coding theory plays an important role. Among them, cyclic codes have attracted much attention because of their good algebraic structure and easy analysis performance. In this paper, we will study one class of cyclic codes over F3. Given the length and dimension, we show that it is optimal by proving its minimum distance is equal to 4, according to the Sphere Packing bound.
References
[1]
Ding, C.S. and Helleseth, T. (2013) Optimal Ternary Cyclic Codes from Monomials. IEEE Transactions on Information Theory, 59, 5898-5904. https://doi.org/10.1109/TIT.2013.2260795
[2]
Han, D.C. and Yan, H.D. (2019) On an Open Problem about a Class of Optimal Ternary Cyclic Codes. Finite Fields and Their Applications, 59, 335-343. https://doi.org/10.1016/j.ffa.2019.07.002
[3]
Zha, Z.B. and Hu, L. (2020) New Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four. Finite Fields and Their Applications, 64, Article ID: 101671. https://doi.org/10.1016/j.ffa.2020.101671
[4]
Zhou, Z.C. and Ding, C.S. (2014) A Class of Three-Weight Cyclic Codes. Finite Fields and Their Applications, 25, 79-93. https://doi.org/10.1016/j.ffa.2013.08.005
[5]
Fan, C.L., Li, N. and Zhou, Z.C. (2016) A Class of Optimal Ternary Cyclic Codes and Their Duals. Finite Fields and Their Applications, 37, 193-202. https://doi.org/10.1016/j.ffa.2015.10.004
[6]
Liu, Y., Cao, X.W. and Lu, W. (2021) Two Classes of New Optimal Ternary Cyclic Codes. Advances in Mathematics of Communications, 17, 979-993. https://doi.org/10.3934/amc.2021033
[7]
Zha, Z.B., Hu, L., Liu, Y. and Cao, X.W. (2021) Further Results on Optimal Ternary Cyclic Codes. Finite Fields and Their Applications, 75, Article ID: 101898. https://doi.org/10.1016/j.ffa.2021.101898
[8]
Huffman, W.C. and Pless, V. (2010) Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge.
[9]
Van Lint, J.H. (1998) Coding Theory. Elsevier, Netherlands, 773-807.
[10]
Lidl, R. and Niederreiter, H. (1997) Finite Fields. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511525926
