English

Cyclic Difference Sets And Cyclic Hadamard Matrices

Number Theory 2011-12-21 v6

Abstract

The collection of cyclic Hadamard matrices {H = (a_{i - j}) : 0 <= i, j < n, and a_i = -1, 1} of order n is characterized by the orthogonality relation HH^T = nI. Only two of such matrices are currently known. It will be shown that this collection consists of precisely two matrices. An application of this result implies that there are exactly seven Barker sequences over the binary set {-1, 1}.

Keywords

Cite

@article{arxiv.1110.1322,
  title  = {Cyclic Difference Sets And Cyclic Hadamard Matrices},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:1110.1322},
  year   = {2011}
}

Comments

Simpler And Improved Version, 8 Pages

R2 v1 2026-06-21T19:16:13.246Z