Research on codes, lattices, and vertex operator algebras using design theory

2012 Fiscal Year Final Research Report

• Project/Area Number: 22840003
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yamagata University (2011-2012); Tohoku University (2010)
• Principal Investigator: MIEZAKI Tsuyoshi 山形大学, 地域教育文化学部, 講師 (60584068)
• Project Period (FY): 2010 – 2012
• Keywords: 代数的組合せ論 / 符号 / 格子 / 頂点作用素代数 / 保型形式 / モックテータ関数 / フーリエ係数 / デザイン理論

Research Abstract

Codes, Lattices, and Vertex Operator Algebras are important mathematical objects with many similar properties. For example, designs and minimum distances are defined on the three objects. Originally, the coding theory was introduced for the purpose of communication, hence, it has wide application in real life. In this study, I investigated some property of the three objects for some cases. For example, I determined the minimum bounds and classified t-designs for some cases.

Research Products

• [Journal Article] On a generalization of spherical designs (2013)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Discrete Math Volume: 313no. 4 Pages: 375-380
  • DOI: DOI:10.1016/j.disc.2012.11.012
  • Peer Reviewed
• [Journal Article] Conformal designs and D.H Lehmer's conjecture (2013)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: J. Algebra Volume: 374 Pages: 59-65
  • DOI: DOI:10.1016/j.jalgebra.2012.10.019.
  • Peer Reviewed
• [Journal Article] Frames in the odd Leech lattice (2012)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: J. Number Theory Volume: 132 no. 12 Pages: 2773-2778
  • DOI: DOI:10.1016/j.jnt.2012.05.030.
  • Peer Reviewed
• [Journal Article] On Euclidean designs and potential energy (2012)
  • Author(s): Tsuyoshi Miezaki, Makoto Tagami
  • Journal Title: Electron. J. Combin Volume: 19 no. 1 Pages: 2,18
  • URL: http://arxiv.org/pdf/1109.2226.pdf
  • Peer Reviewed
• [Journal Article] On the Mathieu mock theta function (2012)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Proc.Japan Acad.Ser. A Math. Sci Volume: 88no. 2
  • DOI: DOI:10.3792/pjaa.88.28
  • Peer Reviewed
• [Journal Article] On a property of 2-dimensional integral Euclidean lattices (2012)
  • Author(s): Eiichi Bannai, Tsuyoshi Miezaki
  • Journal Title: J. Number Theory132 Volume: no. 3 Pages: 371-378
  • DOI: DOI:10.1016/j.jnt.2011.07.011
  • Peer Reviewed
• [Journal Article] An elementary approach to toy models for D.H. Lehmer's conjecture (Russian) (2011)
  • Author(s): Eiichi Bannai, Tsuyoshi Miezak,Vladimir A. Yudin
  • Journal Title: Izv. Ross. Akad. Nauk Ser. Mat75 Volume: no. 6 Pages: 3-16
  • Peer Reviewed
• [Journal Article] An Optimal Odd Unimodular Lattice in Dimension 72 (2011)
  • Author(s): Masaaki Harada ,Tsuyoshi Miezaki
  • Journal Title: Arch. Math. (Basel)97 Volume: no.6 Pages: 529-533
  • DOI: doi:10.1007/s00013-011-0333-3
  • Peer Reviewed
• [Journal Article] An Upper Bound on the Minimum Weight of Type II Z_<2k>-Codes (2011)
  • Author(s): Masaaki Harada, Tsuyoshi Miezaki
  • Journal Title: J. Combin. Theory, Ser. A 118 Volume: no.1 Pages: 190-196
  • DOI: doi:10.1016/j.jcta.2010.02.007
  • Peer Reviewed
• [Journal Article] Nonexistence for extremal Type II Z_<2k>-Codes (2010)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Kumamoto J. Math. 23 Pages: 27-35
  • URL: http://arxiv.org/pdf/0908.3185.pdf.
  • Peer Reviewed
• [Presentation] The McKay-Thompson series of Mathieu moonshine modulo two (2013)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 日本数学会年会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-22
• [Presentation] マシュー群に関連した擬テータ関数に現れる合同式 (2013)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 研究集会「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: 京都大学数理解析研究所
  • Year and Date: 2013-01-07
• [Presentation] 有限群に関連した擬テータ関数に現れる合同式 (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 談話会
  • Place of Presentation: 近畿大学
  • Year and Date: 2012-12-21
• [Presentation] On the existence of extremal Type II Z_<2k>-codes (2012)
  • Organizer: 南九州代数系集会
  • Place of Presentation: 熊本大学
  • Year and Date: 2012-08-31
• [Presentation] 符号と格子 (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 数学オリンピック財団主催夏季セミナー
  • Place of Presentation: ヴィラ千ヶ滝
  • Year and Date: 2012-08-24
• [Presentation] On the existence of extremal Type II Z2k-codes (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第29回代数的組合せ論研究集会
  • Place of Presentation: 弘前大学
  • Year and Date: 2012-06-18
• [Presentation] Mathieu moonshine 現象における擬テータ関数 (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 日本数学会2012 年度年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-26
• [Presentation] On the Mathieu mock theta function (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Algebra Seminar, RWTH Aachen University
  • Place of Presentation: ドイツ
  • Year and Date: 2012-03-21
• [Presentation] Mathieu moonshine 現象における擬テータ関数 (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第164回数理情報科学談話会
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2012-03-09
• [Presentation] 符号とデザイン (2011)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 小研究集会「有限幾何学とその周辺」
  • Place of Presentation: 大分大学
  • Year and Date: 2011-12-10
• [Presentation] 格子の性質「Universally Concyclic 」について (2011)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第23回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2011-07-31
• [Presentation] Conformal designs based on lattice vertex operator algebras (2011)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Japan-Korea Workshop on Algebra and Combinatorics
  • Place of Presentation: 東北大学
  • Year and Date: 2011-01-25
• [Presentation] Toy models for D. H. Lehmer's conjecture (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Algebra Seminar, Kansas State University
  • Place of Presentation: アメリカ
  • Year and Date: 2010-11-29
• [Presentation] An upper bound of minimum weight of Type II Z_<2k>-codes Combinatorics seminer (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Beijing Normal University
  • Place of Presentation: 中国
  • Year and Date: 2010-10-22
• [Presentation] An upper bound of minimum weight of Type II Z_<2k>-codes (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Combinatorics seminer,Hebei Normal University
  • Place of Presentation: 中国
  • Year and Date: 2010-10-19
• [Presentation] ルート格子D4 に付随した格子頂点作用素代数の共形デザインについて (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第22回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2010-07-31
• [Presentation] 4 次直交群の有限部分群から構成される球面デザインについて (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第27回代数的組合せ論シンポジウム
  • Place of Presentation: 高知大学
  • Year and Date: 2010-06-21
• [Presentation] Type II Z_<2k>-符号の最小距離の上界 (2010)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 及びその上界を達成する符号の非存在について, 数理科学セミナー
  • Place of Presentation: 高知大学
  • Year and Date: 2010-06-19
• [Remarks]
  • URL: https://sites.google.com/site/tmiezaki/