Notes on the value function (Q849349)

The purpose of this paper is to show some important properties of the value function, and then apply them to linear codes. In fact, the value function was first introduced by \textit{W. Chen} and \textit{T. Kløve} [IEEE Trans. Inf. Theory 42, No. 6, Pt. 2, 2265--2272 (1996; Zbl 0872.94044)], and it was used to construct the generator matrix of a linear code so as to determine the generalized Hamming weight. The relative generalized Hamming weight was first introduced in 2005 by Luo, Chaichana, Han Vinck and Chen [\textit{Y. Luo}, IEEE Trans. Inf. Theory 51, No. 3, 1222--1229 (2005; Zbl 1297.94035)]. The value function can also be generalized to study the relative generalized Hamming weight of a linear code and its subcodes.