Designs in Additive Codes over GF (4)

Abstract

The purpose of this paper is to study designs in additive codes over GF(4). There are two types of designs. One is a classical t-design with repeated blocks. In this case we have an analog of the Assmus–Mattson Theorem for additive codes over GF(4). The other is a generalized t-design first introduced by Delsarte [4]. As an example, we consider the dodecacode, which is the unique additive even self-dual (12, 212, 6) code. We show that there exists a 5-(12, 6, 3) design in the dodecacode with either 3 distinct blocks or 3 repeated blocks covering a 5-set. We also find a new simple 3-(11, 5, 4) design in the shortened dodecacode by a computer search. Additionally we show that any extremal additive even self-dual code over GF(4) is homogeneous.