New bounds on the minimum distance of cyclic codes (Q2025340)

Estimating the minimum distance is one of the biggest questions in coding theory. The authors give us improved bounds on the minimum distance of cyclic codes. The main focus is generalization of the bounds found in [\textit{A. Zeh} et al., ``Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes'', in: Proceedings of the IEEE international symposium on information theory, ISIT 2013, Istanbul, Turkey, July 7--12, 2013. Piscataway, NJ: IEEE. 126--130 (2013; \url{doi:10.1109/ISIT.2013.6620201})] and their improvement. Two new lower bounds on the minimum distance of a given cyclic code are shown. The first improvement is established using cyclic product code and the second new bound is shown by applying the method of the non-zero-locator code. Lastly, examples found using long binary arrays (which has decreased the huge amount of computational time for finding them) for both bounds are presented.