Quasi-unbiased hadamard matrices and weakly unbiased hadamard matrices: A coding-theoretic approach

Makoto Araya, Masaaki Harada, Sho Suda

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper is concerned with quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices, which are generalizations of unbiased Hadamard matrices, equivalently unbiased bases. These matrices are studied from the viewpoint of coding theory. As a consequence of a codingtheoretic approach, we provide upper bounds on the number of mutually quasiunbiased Hadamard matrices. We give classifications of a certain class of selfcomplementary codes for modest lengths. These codes give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. Some modification of the notion of weakly unbiased Hadamard matrices is also provided.

Original languageEnglish
Pages (from-to)951-984
Number of pages34
JournalMathematics of Computation
Volume86
Issue number304
DOIs
Publication statusPublished - 2017

Keywords

  • Selfcomplementary code
  • Unbiased Hadamard matrix
  • Unbiased weighing matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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