Combinatorial equivalence of (0, 1) circulant matrices

✍ Scribed by Melvin A. Breuer

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 599 KB
• Volume: 3
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(69)80004-8

✦ Synopsis

In this paper various properties of (0, 1) square matrices are investigated, and in particular, circulant matrices are considered. If r is a (0, 1) vector or code word of length n and contains exactly K one elements, then let A(r) be the corresponding circulant matrix having r as its first row. In particular, if in r the K one elements are in the first K positions, then we say that A(r) is a canonical matrix with parameters (K, n). Two matrices A and A' are said to be in the same equivalence class if there exist permutation matrices P and P' such that A" ~ PAP', and we write A ~ A'. We assume that no matrix A being considered is equivalent to a matrix A' of the form