Projective spaces and quasi-cyclic codes (Q2715947)

The incidence matrix of a finite projective plane of order \(q\) can be arranged as a circulant matrix with ones on the diagonal. By appending a unit matrix one obtains a generating matrix for a binary code that is studied in the paper. It is a double circulant \([2(q^2 + q +1), q^2+ q + 1, q+2]\)-code, and, if \(q\) is odd, by omitting the odd-weight codewords one gets a doubly even \([2(q^2 + q + 1), q^2+q, 2(q+1)]\) self-orthogonal code. By adding the all-ones codeword one then receives a self-dual code. The paper contains a lot of examples, and some conjectures.