Study on Hadamard matrices based on algebraic combinatorics

• Project/Area Number: 15K21075
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics; Algebra
• Research Institution: Aichi University of Education
• Principal Investigator: Suda Sho 愛知教育大学, 教育学部, 講師 (30710206)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: アダマール行列 / アソシエーションスキーム / mutually unbiased base / 複素アダマール行列 / orthogonal design / EW tournament / 一般化アダマール行列 / conference matrix / 直交デザイン / 不偏相互基底

Outline of Final Research Achievements

I have studied combinatorial structures related to Hadamard matrices. By introducing the concepts of linked systems of symmetric group divisible designs and unbiased orthogonal designs, unifying methods to study the previous works are developed. Moreover, association schemes based on finite fields are constructed.

Research Products

• [Int'l Joint Research] University of Lethbridge(カナダ)
• [Int'l Joint Research] Nanyang Technological University(シンガポール)
• [Int'l Joint Research] Brown University(米国)
• [Int'l Joint Research] レスブリッジ大学(カナダ)
• [Journal Article] On a class of quaternary complex Hadamard matrices (2018)
  • Author(s): Fender Kai, Kharaghani Hadi, Suda Sho
  • Journal Title: Discrete Math. Volume: 341 Issue: 2 Pages: 421-426
  • DOI: 10.1016/j.disc.2017.09.009
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Non-commutative association schemes and their fusion association schemes (2018)
  • Author(s): Hadi Kharaghani, Sho Suda
  • Journal Title: Finite Fields and Their Applications Volume: 52 Pages: 108-125
  • DOI: 10.1016/j.ffa.2018.03.007
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Unbiased orthogonal designs (2018)
  • Author(s): Kharaghani Hadi, Suda Sho
  • Journal Title: Des. Codes Cryptogr. Volume: 86 Issue: 7 Pages: 1573-1588
  • DOI: 10.1007/s10623-017-0414-9
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Linked systems of symmetric group divisible designs (2017)
  • Author(s): Kharaghani Hadi, Suda Sho
  • Journal Title: J. Algebraic Combin. Volume: 47 Issue: 2 Pages: 319-343
  • DOI: 10.1007/s10801-017-0777-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A strongly regular decomposition of the complete graph and its association scheme (2017)
  • Author(s): Hadi Kharaghani, Sara Sasani, Sho Suda
  • Journal Title: Finite Fields Appl. Volume: 48 Pages: 356-370
  • DOI: 10.1016/j.ffa.2017.08.012
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Symmetric and skew-symmetric {0,±1}-matrices with large determinants (2017)
  • Author(s): Gary Greaves, Sho Suda
  • Journal Title: J. Combin. Des. Volume: 25 Issue: 11 Pages: 507-522
  • DOI: 10.1002/jcd.21567
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Conference matrices with maximum excess and two-intersection sets (2017)
  • Author(s): Koji Momihara, Sho Suda
  • Journal Title: Integers Volume: 17, A 30 Pages: 1-15
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Hoffman's clique bound for normal regular digraphs, and nonsymmetric association schemes (2017)
  • Author(s): Hadi Kharaghani, Sho Suda
  • Journal Title: Mathematics Across Contemporary Sciences, Springer Proc. Math. Stat. Volume: 190 Pages: 137-150
  • DOI: 10.1007/978-3-319-46310-0_8
  • ISBN: 9783319463094, 9783319463100
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Complex spherical codes with two inner products (2016)
  • Author(s): Hiroshi Nozaki and Sho Suda
  • Journal Title: European J. Combin. Volume: 51 Pages: 511-518
  • DOI: 10.1016/j.ejc.2015.07.016
  • NAID: 120006383477
  • Peer Reviewed / Open Access
• [Journal Article] Symemtric Bush-type generalized Hadamard matrices and association schemes (2016)
  • Author(s): Hadi Kharaghani and Sho Suda
  • Journal Title: Finite Fields and Their Applications Volume: 37 Pages: 72-84
  • DOI: 10.1016/j.ffa.2015.09.003
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Supplementary difference sets related to a certain class of complex spherical 2-codes (2016)
  • Author(s): Makoto Araya, Masaaki Harada and Sho Suda
  • Journal Title: Australas. J. Combinatorics Volume: 65 Pages: 71-83
  • Peer Reviewed / Open Access
• [Journal Article] Mutually unbiased Bush-type Hadamard matrices and association schemes (2015)
  • Author(s): Hadi Kharaghani, Sara Sasani and Sho Suda
  • Journal Title: Electronical Journal of Combinatorics Volume: 22
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On relative t-designs in polynomial association schemes (2015)
  • Author(s): Eiichi Bannai, Etsuko Bannai, Sho Suda and Hajime Tanaka
  • Journal Title: Electronical Journal of Combinatorics Volume: 22
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod 4) (2018)
  • Author(s): Sho Suda
  • Organizer: 日本数学会応用数学分科会
• [Presentation] Association schemes obtained from twin prime powers (2017)
  • Author(s): Sho Suda
  • Organizer: Japan-Korea Workshop on Algebra and Combinatorics
  • Place of Presentation: 熊本大学（熊本県熊本市）
  • Year and Date: 2017-02-09
  • Int'l Joint Research / Invited
• [Presentation] Skew-symmetric EW matrices and tournaments (2017)
  • Author(s): Sho Suda
  • Organizer: Special Western Canada Linear Algebra meeting
  • Int'l Joint Research / Invited
• [Presentation] Skew-symmetric EW matrices and tournaments (2017)
  • Author(s): Sho Suda
  • Organizer: Japan Conference on Combinatorics and its Applications (JCCA-2017)
• [Presentation] On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod 4) (2017)
  • Author(s): Sho Suda
  • Organizer: International Workshop on Bannai-Ito Theory
  • Int'l Joint Research / Invited
• [Presentation] On the Smith normal form of a skew-symmetric D-optimal design of order n≡2 (mod 4) (2017)
  • Author(s): Sho Suda
  • Organizer: Research on algebraic combinatorics and representation theory of finite groups and vertex operator algebras
  • Invited
• [Presentation] Linked systems of symmetric group divisible designs (2016)
  • Author(s): Sho Suda
  • Organizer: CMS Algebraic Design Theory
  • Place of Presentation: アルバータ（カナダ）
  • Year and Date: 2016-06-27
  • Int'l Joint Research / Invited
• [Presentation] Unbiased orthogonal designs (2016)
  • Author(s): Sho Suda
  • Organizer: JCCA 2016: The Japanese Conference on Combinatorics and its Applications
  • Place of Presentation: 京都大学（京都府京都市）
  • Year and Date: 2016-05-24
  • Int'l Joint Research
• [Presentation] Unbiased orthogonal designs (2016)
  • Author(s): Sho Suda
  • Organizer: Mini-Workshop "Algebraic Combinatorics and Related Topics"
  • Place of Presentation: 東北大学（宮城）
  • Year and Date: 2016-03-09
• [Presentation] 整数距離集合について (2016)
  • Author(s): 須田庄
  • Organizer: Kunitachi One-Day Symposium on the Recent Developments in the Mathematical Science
  • Place of Presentation: 一橋大学（東京）
  • Year and Date: 2016-02-06
• [Presentation] Introduction to complex spherical codes and designs with applications to MUBs and SIC-POVMs (2015)
  • Author(s): Sho Suda
  • Organizer: Systems of Lines
  • Place of Presentation: ウースター（アメリカ）
  • Year and Date: 2015-08-12
  • Int'l Joint Research / Invited
• [Presentation] 複素球面上の内積集合について (2015)
  • Author(s): 須田庄
  • Organizer: Designs, Codes, Graphs and Related Areas
  • Place of Presentation: 京都大学（京都）
  • Year and Date: 2015-07-09
• [Presentation] Association schemes related to Hadamard matrices (2015)
  • Author(s): Sho SUda
  • Organizer: 8-th Slovenian Conference on Graph Theory
  • Place of Presentation: クランスカ・ゴーラ（スロベニア）
  • Year and Date: 2015-06-25
  • Int'l Joint Research
• [Presentation] Complex spherical codes and linear programming bounds (2015)
  • Author(s): Sho Suda
  • Organizer: 2015 Workshop on Combinatorics and Applications
  • Place of Presentation: 上海（中国）
  • Year and Date: 2015-04-23
  • Int'l Joint Research