The Invariants of the Clifford Groups
نویسندگان
چکیده
The automorphism group of the Barnes-Wall lattice Lm in dimension 2 m (m 6= 3) is a subgroup of index 2 in a certain “Clifford group” of structure 2 + .O (2m, 2). This group and its complex analogue CIm of structure (2 + YZ8).Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge’s 1996 result that the space of invariants for Cm of degree 2k is spanned by the complete weight enumerators of the codes C ⊗ F2m, where C ranges over all binary self-dual codes of length 2k; these are a basis if m ≥ k − 1. We also give new constructions for Lm and Cm: let M be the Z[ √ 2]-lattice with Gram matrix
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 24 شماره
صفحات -
تاریخ انتشار 2001