Projective Spaces and Quasi-Cyclic Codes

T.Aaron Gulliver1, Vijay K.Bhargava2
1Department of Electrical and Electronic Engineering, University of Canterbury, Christchurch, New Zealand,
2 Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, MS 8610, Victoria, B.C., Canada V8W 3P6,

Abstract

A family of double circulant quasi-cyclic codes is constructed from the incidence matrices of difference sets associated with hyperplanes in projective space. A subset of these codes leads to a class of doubly-even self-orthogonal codes, and two classes of self-dual codes.