Uniqueness of Butson Hadamard matrices of small degrees

Mitsugu Hirasaka, Kyoung Tark Kim, Yoshihiro Mizoguchi

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let BHn×n(m) be the set of n×n Butson Hadamard matrices where all the entries are m-th roots of unity. For H1,H2∈BHn×n(m), we say that H1 is equivalent to H2 if H1=PH2Q for some monomial matrices P and Q whose nonzero entries are m-th roots of unity. In the present paper we show by computer search that all the matrices in BH17×17(17) are equivalent to the Fourier matrix of degree 17. Furthermore we shall prove that, for a prime number p, a matrix in BHp×p(p) which is not equivalent to the Fourier matrix of degree p gives rise to a non-Desarguesian projective plane of order p.

    Original languageEnglish
    Pages (from-to)70-77
    Number of pages8
    JournalJournal of Discrete Algorithms
    Volume34
    DOIs
    Publication statusPublished - Sep 1 2015

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics

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