Remarks on s-extremal codes
Jon-Lark Kim · Series on coding theory and cryptology · 2007
We study s-extremal codes over F4 or over F2. A Type I self-dual code over F4 or over F2 of length n and minimum distance d is s-extremal if the minimum weight of its shadow is largest possible. The purpose of this paper is to give some results which are missing in a series of papers by Bachoc and Gaborit [2], by Gaborit [6], and by Bautista, et. al. [1]. In particular, we give an explicit formula for the numbers of the first four nonzero weights of an s-extremal code over F4. We improve a bound on the length for which there exists an s-extremal code over F4 (res. F2) with even minimum distance d (resp. d ≡ 0 (mod 4)), and give codes related to s-extremal binary codes.