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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: A coding-theoretic approach
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by Makoto Araya, Masaaki Harada and Sho Suda PDF
Math. Comp. 86 (2017), 951-984 Request permission

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 coding-theoretic approach, we provide upper bounds on the number of mutually quasi-unbiased Hadamard matrices. We give classifications of a certain class of self-complementary 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.
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Additional Information
  • Makoto Araya
  • Affiliation: Department of Computer Science, Shizuoka University, Hamamatsu 432–8011, Japan
  • MR Author ID: 609178
  • Email: araya@inf.shizuoka.ac.jp
  • Masaaki Harada
  • Affiliation: Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980–8579, Japan
  • Email: mharada@m.tohoku.ac.jp
  • Sho Suda
  • Affiliation: Department of Mathematics Education, Aichi University of Education, Kariya 448-8542, Japan
  • Email: suda@auecc.aichi-edu.ac.jp
  • Received by editor(s): April 6, 2015
  • Received by editor(s) in revised form: September 16, 2015, and September 30, 2015
  • Published electronically: June 29, 2016

  • Dedicated: Dedicated to Professor Satoshi Yoshiara on his 60th birthday
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 951-984
  • MSC (2010): Primary 05B20, 94B25, 94B65; Secondary 05E30
  • DOI: https://doi.org/10.1090/mcom/3122
  • MathSciNet review: 3584556