Constructions of spherical designs using finite groups and lattices

• Project/Area Number: 26400003
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: Munemasa Akihiro 東北大学, 情報科学研究科, 教授 (50219862)
• Co-Investigator(Kenkyū-buntansha): 須田 庄 愛知教育大学, 教育学部, 講師 (30710206) ; 三枝崎 剛 山形大学, 地域教育文化学部, 准教授 (60584068) ; 篠原 雅史 滋賀大学, 教育学部, 講師 (70432903) ; 野崎 寛 愛知教育大学, 教育学部, 講師 (80632778)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 球デザイン / グラフ / 整数格子 / 有限群 / 線形符号 / 代数的組合せ論 / 組合せデザイン / グラフ理論 / 有限体

Outline of Final Research Achievements

In connection with spherical designs, we investigated spectra of graphs and finite permutation groups. We have found a highly nontrivial method of switching for constructing cospectral mates of graphs to give an alternative construction of the twisted Grassmann graphs. Other achievements includes extension of previously known properties of subsets of a sphere derived from association schemes.

Research Products

• [Journal Article] Distance sets on circles (2017)
  • Author(s): Momihara, K. and Shinohara, M.
  • Journal Title: American Mathematical Monthly Volume: 124 Issue: 3 Pages: 241-254
  • DOI: 10.4169/amer.math.monthly.124.3.241
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A note on the Brawley-Carlitz theorem on irreducibility of composed products of polynomials over finite fields (2017)
  • Author(s): Akihiro Munemasa, Hiroko Nakamura
  • Journal Title: Lecture Notes in Computer Science Volume: 10064 Pages: 84-92
  • DOI: 10.1007/978-3-319-55227-9_7
  • ISBN: 9783319552262, 9783319552279
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Godsil-McKay switching and twisted Grassmann graphs (2017)
  • Author(s): Akihiro Munemasa
  • Journal Title: Designs, Codes and Cryptography Volume: 84 Issue: 1-2 Pages: 173-179
  • DOI: 10.1007/s10623-016-0244-1
  • Peer Reviewed
• [Journal Article] Transforming a Matrix into a Standard Form (2017)
  • Author(s): Akihiro Munemasa, Pritta Etriana Putri
  • Journal Title: Interdisciplinary Information Sciences Volume: 23 Issue: 2 Pages: 163-166
  • DOI: 10.4036/iis.2016.S.02
  • NAID: 130006287946
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access
• [Journal Article] An upper bound of the value of t of the support t-designs of extremal binary doubly even self-dual codes (2016)
  • Author(s): Tsuyoshi Miezaki, Hiroyuki Nakasora
  • Journal Title: Designs, Codes and Cryptography Volume: 79 Issue: 1 Pages: 37-46
  • DOI: 10.1007/s10623-014-0033-7
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Multiply union families in N^n (2016)
  • Author(s): P.Frankl, M.Shinohara, N.Tokushige
  • Journal Title: European Journal of Combinatorics Volume: 58 Pages: 66-74
  • DOI: 10.1016/j.ejc.2016.05.007
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Distance sets and Kneser's theorem (2016)
  • Author(s): 篠原雅史, 籾原幸二
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2003 Pages: 96-103
• [Journal Article] Few triangle sets (2016)
  • Author(s): 篠原雅史, 平坂貢
  • Journal Title: 第33回代数的組合せ論シンポジウム報告集 Volume: 33 Pages: 1-6
  • Int'l Joint Research
• [Journal Article] On the Classification of Self-Dual \mathbb{Z}_<i>k</i>-Codes II (2016)
  • Author(s): Masaaki Harada, Akihiro Munemasa
  • Journal Title: Interdisciplinary Information Sciences Volume: 22 Issue: 1 Pages: 81-85
  • DOI: 10.4036/iis.2015.R.01
  • NAID: 130005281142
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access
• [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
• [Presentation] Few triangle sets (2017)
  • Author(s): 篠原雅史
  • Organizer: 直観幾何学2017
  • Place of Presentation: 熊本大学（熊本市）
  • Year and Date: 2017-02-12
• [Presentation] Association schemes obtained from twin prime powers (2016)
  • Author(s): 須田庄
  • Organizer: Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
  • Place of Presentation: The Univeristy of Newcastle（オーストラリア）
  • Year and Date: 2016-12-14
  • Int'l Joint Research
• [Presentation] Largest regular multigraphs with three distinct eigenvalues (2016)
  • Author(s): 野崎寛
  • Organizer: Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
  • Place of Presentation: The University of Newcastle city campus（オーストラリア）
  • Year and Date: 2016-12-05
• [Presentation] Largest regular digraphs with three eigenvalues (2016)
  • Author(s): 野崎寛
  • Organizer: International Workshop on Algebraic Combinatorics
  • Place of Presentation: Anhui University（中国）
  • Year and Date: 2016-10-29
• [Presentation] Group theoretic aspects of the theory of association schemes (2016)
  • Author(s): 宗政昭弘
  • Organizer: International Workshop on Algebraic Combinatorics
  • Place of Presentation: Anhui University（中国）
  • Year and Date: 2016-10-29
  • Int'l Joint Research / Invited
• [Presentation] Affine resolvable designs and an extension of linked symmetric designs (2016)
  • Author(s): 須田庄
  • Organizer: International Workshop on Algebraic Combinatorics
  • Place of Presentation: Anhui University（中国）
  • Year and Date: 2016-10-28
  • Int'l Joint Research
• [Presentation] 少ない非合同三角形を持つ点配置について (2016)
  • Author(s): 篠原雅史
  • Organizer: 組合せ論サマーセミナー2016
  • Place of Presentation: 下呂市民会館（岐阜県下呂市）
  • Year and Date: 2016-08-26
• [Presentation] Triply even codes obtained from some graphs and finite geometries (2016)
  • Author(s): 宗政昭弘
  • Organizer: Graphs and Groups, Spectra and Symmetries
  • Place of Presentation: Novosibirsk State University（ロシア）
  • Year and Date: 2016-08-21
  • Int'l Joint Research / Invited
• [Presentation] Structures of minimal two-distance sets of complete multipartite graphs (2016)
  • Author(s): 篠原雅史
  • Organizer: 78th KPPY Combinatorics Workshop
  • Place of Presentation: Pusan National University（韓国）
  • Year and Date: 2016-08-02
  • Int'l Joint Research
• [Presentation] Few triangle sets (2016)
  • Author(s): 篠原雅史
  • Organizer: 第33回代数的組合せ論シンポジウム
  • Place of Presentation: ピアザ淡海（滋賀県大津市）
  • Year and Date: 2016-06-23
• [Presentation] デザイン理論について (2016)
  • Author(s): 三枝崎剛
  • Organizer: 大阪組合せ論セミナー
  • Place of Presentation: 大阪市立大学梅田サテライト（大阪市）
  • Year and Date: 2016-06-18
• [Presentation] Maximal m-distance sets containing the representation of the Hamming graph H(n,m) (2016)
  • Author(s): 野崎寛
  • Organizer: The Japanese Conference on Combinatorics and its Applications
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2016-05-25
  • Int'l Joint Research
• [Presentation] Maximum Euclidean sets that contain few non-congruent triangles (2016)
  • Author(s): 篠原雅史
  • Organizer: 76th KPPY Combinatorics Workshop
  • Place of Presentation: Pusan National University（韓国）
  • Year and Date: 2016-04-30
  • Int'l Joint Research
• [Presentation] 組合せ論におけるいくつかの分類問題について (2016)
  • Author(s): 篠原雅史
  • Organizer: 大阪組合せ論セミナー
  • Place of Presentation: 大阪市立大学梅田サテライト（大阪市）
  • Year and Date: 2016-04-16
• [Presentation] Unbiased orthogonal designs (2016)
  • Author(s): 須田庄
  • Organizer: 代数的組合せ論とその周辺
  • Place of Presentation: 東北大学（仙台市）
  • Year and Date: 2016-03-09
• [Presentation] Multiply union families in N^n (2016)
  • Author(s): 篠原雅史
  • Organizer: Korea-Japan Workshop on Algebra and Combinatorics
  • Place of Presentation: 釜山国立大学、韓国
  • Year and Date: 2016-01-29
  • Int'l Joint Research
• [Presentation] Distance sets and Kneser's theorem (2016)
  • Author(s): 篠原雅史
  • Organizer: 有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2016-01-07
• [Presentation] On the largest subsets avoiding the diameter of (0,1,-1)-vectors (2016)
  • Author(s): 野崎寛
  • Organizer: 有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2016-01-07
• [Presentation] Covering radii and shadows of binary self-dual codes (2015)
  • Author(s): 宗政昭弘
  • Organizer: 代数学と計算
  • Place of Presentation: 首都大学東京（東京都）
  • Year and Date: 2015-12-15
• [Presentation] Self-orthogonal designs and equitable partitions (2015)
  • Author(s): 宗政昭弘
  • Organizer: 計算代数システムによる新しい数学の開拓と進展
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2015-09-30
• [Presentation] Self-orthogonal designs and equitable partitions (2015)
  • Author(s): 宗政昭弘
  • Organizer: Algebraic Combinatorics Workshop
  • Place of Presentation: 浙江大学（中国）
  • Year and Date: 2015-09-20
  • Int'l Joint Research / Invited
• [Presentation] 円周上の距離集合について (2015)
  • Author(s): 篠原雅史
  • Organizer: 離散数学とその応用研究集会 2015
  • Place of Presentation: 熊本大学（熊本市）
  • Year and Date: 2015-08-23
• [Presentation] Introduction to complex spherical codes and designs with applications to MUBs and SIC-POVMs (2015)
  • Author(s): 須田庄
  • Organizer: Systems of Lines: Applications of Algebraic Combinatorics
  • Place of Presentation: Worcester Polytechnic Institute, U.S.A.
  • Year and Date: 2015-08-12
  • Int'l Joint Research
• [Presentation] Richard Thompson's group F (2015)
  • Author(s): 宗政昭弘
  • Organizer: 有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス（群馬県）
  • Year and Date: 2015-08-03
• [Presentation] 複素球面上の内積集合について (2015)
  • Author(s): 須田庄
  • Organizer: デザイン、符号、グラフおよびその周辺
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2015-07-09
• [Presentation] A parametric family of complex Hadamard matrices (2014)
  • Author(s): 宗政昭弘
  • Organizer: 実験計画法およびその周辺の組合せ構造
  • Place of Presentation: 城崎国際アートセンター
  • Year and Date: 2014-12-15
• [Presentation] Q多項式スキーム (2014)
  • Author(s): 須田庄
  • Organizer: 代数的組合せ論夏の学校
  • Place of Presentation: 秋保リゾートホテルクレセント
  • Year and Date: 2014-06-17
• [Presentation] アソシエーションスキーム入門 (2014)
  • Author(s): 宗政昭弘
  • Organizer: 代数的組合せ論夏の学校
  • Place of Presentation: 秋保リゾートホテルクレセント
  • Year and Date: 2014-06-15 – 2014-06-16