Upper bounds on the covering radius of a code with a given dual distance
This paper introduces a new approach to obtaining upper bounds on the covering radius of a binary linear code. The method generalizes an approach presented in [\textit{T. Helleseth}, Discrete Appl. Math. 11, 157-173 (1985; Zbl 0576.94020), the second author, Lect. Notes Comput. 388, 1-12 (1989; Zbl 0678.94012)]. It is based on character sums over finite fields and shows that the degree of a suitable polynomial gives an upper bound on covering radius. Moreover, new upper bounds on covering radius are derived as a function of dual distance and dual-distance width by applying Chebyshev polynomials. These bounds are better than Delorme-Solé-Stokes bounds [\textit{C. Delorme} and \textit{P. Solé}, Eur. J. Comb. 12, No. 2, 95-108 (1991; Zbl 0737.05067)], [\textit{P. Solé} and \textit{P. Stokes}, IEEE Trans. Inf. Theory 39, No. 4, 1195-1203 (1993; Zbl 0809.94023)] and in a certain interval they improve on Tietäväinen's bound [the second author, Des. Codes Cryptography 1, No. 1, 31-46 (1991; Zbl 0734.94020)] as well.
scientific article; zbMATH DE number 871020