Symmetry of Codes, Lattices, and Vertex operator algebras

• Project/Area Number: 24740031
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Yamagata University
• Principal Investigator: MIEZAKI Tsuyoshi 山形大学, 教育文化学部, 准教授 (60584068)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 符号 / 格子 / 頂点作用素代数 / デザイン理論 / 保型形式 / 代数的組合せ論 / 代数学 / モックテータ関数 / フーリエ係数

Outline of Final Research Achievements

The purpose of this study is the classification of the codes, the lattices, and the vertex operator algebras from the point of view of the modular forms and the design theory.

Research Products

• [Journal Article] Congruences for the Fourier coefficients of the Mathieu mock theta function (2015)
  • Author(s): Tsuyoshi Miezaki, Matthias Waldherr
  • Journal Title: J. Number Theory Volume: 148 Pages: 451-462
  • DOI: 10.1016/j.jnt.2014.09.025
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the support designs of extremal binary doubly even self-dual codes, (2014)
  • Author(s): Naoyuki Horiguchi, Tsuyoshi Miezaki, Hiroyuki Nakasora
  • Journal Title: Des. Codes Cryptogr. Volume: 72-3 Issue: 3 Pages: 529-537
  • DOI: 10.1007/s10623-012-9782-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The McKay-Thompson series of Mathieu Moonshine modulo two (2014)
  • Author(s): Thomas Creutzig, Gerald Höhn, Tsuyoshi Miezaki
  • Journal Title: Ramanujan J. Volume: 34-3 Issue: 3 Pages: 319-328
  • DOI: 10.1007/s11139-013-9553-4
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the Existence of Extremal Type II Z2k-Codes (2014)
  • Author(s): Masaaki Harada, Tsuyoshi Miezaki
  • Journal Title: Math. Comp. Volume: 83 Issue: 287 Pages: 1427-1446
  • DOI: 10.1090/s0025-5718-2013-02750-0
  • Peer Reviewed
• [Journal Article] Toy models for D.H. Lehmer's conjecture II (2013)
  • Author(s): Eiichi Bannai, Tsuyoshi Miezaki
  • Journal Title: Dev. Math. Volume: 31 Pages: 1-27
  • DOI: 10.1007/978-1-4614-7488-3_1
  • ISBN: 9781461474876, 9781461474883
  • Peer Reviewed
• [Journal Article] On a generalization of spherical designs (2013)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: Discrete Math Volume: 313no. 4 Issue: 4 Pages: 375-380
  • 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: 10.1016/j.jalgebra.2012.10.019
  • 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 Issue: 2 Pages: 28-30
  • DOI: 10.3792/pjaa.88.28
  • NAID: 40019175405
  • Peer Reviewed
• [Journal Article] On Euclidean designs and potential energy (2012)
  • Author(s): Makoto Tagami, Tsuyoshi Miezaki
  • Journal Title: Electron. J. Combin. Volume: 19
  • Peer Reviewed
• [Journal Article] Frames in the odd Leech lattice (2012)
  • Author(s): Tsuyoshi Miezaki
  • Journal Title: J. Number Theory Volume: 132 no. 12 Issue: 12 Pages: 2773-2778
  • DOI: 10.1016/j.jnt.2012.05.030
  • Peer Reviewed
• [Presentation] 2次形式の表現数と符号理論 (2015)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Intersection of Pure Mathematics and Applied Mathematics VIII: Special
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2015-02-20
  • Invited
• [Presentation] Eisenstein series and E-polynomials (2014)
  • Author(s): Tsuyoshi Miezaki
  • 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: 京都大学数理解析研究所
  • Year and Date: 2014-12-17
  • Invited
• [Presentation] Eisenstein polynomials and Zeta polynomials (2014)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Workshop on Galois point and related topics
  • Place of Presentation: 滋賀大学大津サテライトプラザ
  • Year and Date: 2014-09-13
  • Invited
• [Presentation] デザイン理論から見た，符号，格子及び頂点作用素代数の一つの類似 (2014)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: デザイン、符号、グラフおよびその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-07-24
  • Invited
• [Presentation] E-polynomials and Zeta polynomials (2014)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: Workshop around algebraic combinatorics at Kochi University
  • Place of Presentation: 高知大学
  • Invited
• [Presentation] The McKay-Thompson series of Mathieu Moonshine modulo two (2013)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第３０回代数的組合せ論シンポジウム
  • Place of Presentation: 静岡大学
  • Invited
• [Presentation] 32 次元extremal 2-modular 格子に関する注意 (2013)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 第25回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Invited
• [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
  • Invited
• [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
  • Invited
• [Presentation] On the existence of extremal Type II Z2k-codes (2012)
  • Author(s): Tsuyoshi Miezaki
  • Organizer: 南九州代数系集会
  • Place of Presentation: 熊本大学
  • Invited
• [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: 近畿大学数学講演会
  • Place of Presentation: 京都大学
  • Invited
• [Remarks] Tsuyoshi Miezaki's website
  • URL: https://sites.google.com/site/tmiezaki/
• [Remarks] 三枝崎剛のホームページ
  • URL: https://sites.google.com/site/tmiezakij/
• [Remarks] Tsuyoshi Miezaki's website
  • URL: https://sites.google.com/site/tmiezaki/papers-1
• [Remarks] Tsuyoshi Miezaki's website
  • URL: https://sites.google.com/site/tmiezaki/