Type I Codes over GF(4)

Abstract

It was shown by Gaborit el al. [10] that a Euclidean self-dual code over CF(4) with the property that there is a codeword whose Lee weight 2 (mod 4) is of interest because of its connection to a binary singly-even self-dual code. Such a self-dual code over GF(4) is called Type I. The purpose of this paper is to classify all Type I codes of lengths up to 10 and extremal Type I codes of length 12, and to construct many new extremal Type I codes over GF(4) of lengths from 14 to 22 and 34. As a byproduct, we construct a new extremal singly-even self-dual binary [36, 18,8] code, and a new extremal singly-even self-dual binary [68, 34, 12] code with a previously unknown weight enumerator W-2 for beta = 95 and gamma = 1.