Uniqueness of Butson Hadamard matrices of small degrees

Mitsugu Hirasaka, Kyoung Tark Kim, Yoshihiro Mizoguchi

研究成果: ジャーナルへの寄稿記事

抄録

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.

元の言語英語
ページ(範囲)70-77
ページ数8
ジャーナルJournal of Discrete Algorithms
34
DOI
出版物ステータス出版済み - 9 1 2015

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Hadamard matrices
Hadamard Matrix
Uniqueness
Roots of Unity
P-matrix
Q-matrix
Monomial
Projective plane
Prime number

All Science Journal Classification (ASJC) codes

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

これを引用

Uniqueness of Butson Hadamard matrices of small degrees. / Hirasaka, Mitsugu; Kim, Kyoung Tark; Mizoguchi, Yoshihiro.

:: Journal of Discrete Algorithms, 巻 34, 01.09.2015, p. 70-77.

研究成果: ジャーナルへの寄稿記事

Hirasaka, Mitsugu ; Kim, Kyoung Tark ; Mizoguchi, Yoshihiro. / Uniqueness of Butson Hadamard matrices of small degrees. :: Journal of Discrete Algorithms. 2015 ; 巻 34. pp. 70-77.
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