THE AUTOMORPHISM GROUP OF AN [l&9,8] QUATERNARY CODE

An [18,9,8] code Ce18 over GF(4) was constructed in [6] as an extended cyclic code, and Pless [9] describes the same code as an extended “Q-code”. This code is of particular interest since it is an extremal quaternary code: an [n, n/2, d] self-dual code with d = 2[n/6] + 2 ([6, p. 2951, [3, p. 2051). In the present note we give new coordinates for this code, enabling us to find a simple description of its 2754 minimal weight words and also to determine for the first time its automorphism group G. This group G has structure 3 x (PSI+(16).4) and order 48960, and has two orbits on the coordinates, of sizes 17 and 1. It is interesting that, although G is not transitive on the 18 coordinates, the [17,9,7] punctured codes obtained by deleting any one coordinate all have the same weight enumerator, and even the same complete weight enumerator. We also study the properties of the particular [17,9,7] code %‘$!$) obtained by puncturing the 18th coordinate (the odd-man-out), and its even subcode %?I?, which is a [17,8,8] code. Two other cyclic codes also appear: a [17,4,12] code V#, which is a two-weight code studied by Calderbank and Kantor [l], and its dual, which is a [17,13,4] code V $+“’ The codewords of maximal weight . in %$+), taken modulo scalar multiples, form a complex conference matrix (see Fig. 4). These four codes of length 17 may also be constructed from 17-dimensional