Inequivalence of Nega-cyclic $\pm 1$ Matrices

Abstract

We study nega-cyclic $\pm 1$ matrices. We obtain preliminary results which are then used to decrease the search space. We find that there are $2$, $4$, $9$, $23$, $63$, and $187$ ip-equivalence classes for lengths $3$, $5$, $7$, $9$, $11$, and $13$ respectively. The matrices we find are used in a variant given here of the Goethals-Seidel array to form Hadamard matrices, the aim being to later check them for suitability for CDMA schemes.