Back to Search
Start Over
On equivalence classes of Butson Hadamard matrices BH (4,2k).
- Source :
- Journal of Algebra Combinatorics Discrete Structures & Applications; 2024, Vol. 11 Issue 1, p15-26, 12p
- Publication Year :
- 2024
-
Abstract
- A Butson Hadamard matrix of order n over the k<superscript>th</superscript> root of unity is a square matrix H which entries are some complex k<superscript>th</superscript> root of unity such that HH* = nI<subscript>n</subscript>, where H* is the complex conjugate of H. A set of Butson Hadamard matrices of order n over the k<superscript>th</superscript> root of unity is denoted by BH(n,k). It is well-known that a Butson Hadamard matrices is a generalization of a Hadamard matrix. In this paper, we give some properties of Butson Hadamard matrices of order 4 which implies to the upper and the lower bounds of the number of its equivalence classes. We also showed that the entries of Butson Hadamard matrices of order 4 is 2k-th root of unity for some integer k. Furthermore, we describe the equivalence classes of Butson Hadamard matrices of order 4 by constructing the representative of the class. [ABSTRACT FROM AUTHOR]
- Subjects :
- HADAMARD matrices
Subjects
Details
- Language :
- English
- ISSN :
- 2148838X
- Volume :
- 11
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Algebra Combinatorics Discrete Structures & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 177499869