A New Development of Algebraic Coding Theory

• Project/Area Number: 23340021
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University (2013-2014); Yamagata University (2011-2012)
• Principal Investigator: HARADA Masaaki 東北大学, 情報科学研究科, 教授 (90292408)
• Co-Investigator(Kenkyū-buntansha): MUNEMASA Akihiro 東北大学, 大学院情報科学研究科, 教授 (50219862)
• Co-Investigator(Renkei-kenkyūsha): KITAZUME Masaaki 千葉大学, 大学院理学研究科, 教授 (60204898) ; WADAYAMA Tadashi 名古屋工業大学, 大学院工学研究科, 教授 (20275374) ; ARAYA Makoto 静岡大学, 情報学部, 准教授 (70303526) ; HAGIWARA Manabu 千葉大学, 大学院理学研究科, 准教授 (80415728)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥16,380,000 (Direct Cost: ¥12,600,000、Indirect Cost: ¥3,780,000); Fiscal Year 2014: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2013: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000); Fiscal Year 2012: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000); Fiscal Year 2011: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• Keywords: 組合せ論 / 代数的符号理論 / 自己双対符号 / 格子 / 組合せデザイン / デザイン

Outline of Final Research Achievements

In this research project, I studied algebraic coding theory, especially, self-dual codes. As results, classifications of self-dual codes of length 36 and doubly even self-dual codes of length 40 are completed. Also, I considered the construction of extremal self-dual Z2k-codes.

Research Products

• [Journal Article] On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24 (2015)
  • Author(s): Masaaki Harada
  • Journal Title: Designs, Codes and Cryptogr Volume: 印刷中 Issue: 3 Pages: 373-384
  • DOI: 10.1007/s10623-014-9963-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Extremal Type I Zk-codes and k-frames of odd unimodular lattices (2015)
  • Author(s): Masaaki Harada
  • Journal Title: IEEE Trans. Inform. Theory Volume: 61 Issue: 1 Pages: 72-81
  • DOI: 10.1109/tit.2014.2368563
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Extremal unimodular lattices in dimension 36 (2014)
  • Author(s): Masaaki Harada
  • Journal Title: International J. Combin. Volume: 2014 Pages: 1-7
  • DOI: 10.1155/2014/792471
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups (2014)
  • Author(s): Naoki Chigira, Masaaki Harada and Masaaki Kitazume
  • Journal Title: Designs, Codes and Cryptogr. Volume: 73 Issue: 1 Pages: 33-35
  • DOI: 10.1007/s10623-013-9807-6
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the existence of extremal Type II Z2k-codes (2014)
  • Author(s): Masaaki Harada and Tsuyoshi Miezaki
  • Journal Title: Mathematics of Computation Volume: 83 Pages: 1427-1446
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Residue codes of extremal Type II Z4-codes and the moonshine vertex operator algebra (2013)
  • Author(s): Masaaki Harada, Ching Hung Lam and Akihiro Munemasa
  • Journal Title: Math. Zeitschrift Volume: 274 Issue: 1-2 Pages: 685-700
  • DOI: 10.1007/s00209-012-1091-z
  • Peer Reviewed
• [Journal Article] There is no [21, 5, 14] code over F5 (2013)
  • Author(s): Makoto Araya, Masaaki Harada
  • Journal Title: Discrete Math Volume: 313 Issue: 24 Pages: 2872-2874
  • DOI: 10.1016/j.disc.2013.08.027
  • Peer Reviewed
• [Journal Article] On the existence of extremal Type II Z2k-codes (2013)
  • Author(s): M. Harada, T. Miezaki
  • Journal Title: Mathematics of Computation Volume: 未定
  • Peer Reviewed
• [Journal Article] Some extremal self-dual codes and unimodular lattices in dimension 40 (2013)
  • Author(s): S. Bouyuklieva, I. Bouyukliev, M. Harada
  • Journal Title: Finite Fields and Their Applications Volume: 21 Pages: 67-83
  • DOI: 10.1016/j.ffa.2013.01.009
  • Peer Reviewed
• [Journal Article] Classification of self-dual codes of length 36 (2012)
  • Author(s): M. Harada and A. Munemasa
  • Journal Title: Advances Math. Communications Volume: 6 Issue: 2 Pages: 229-235
  • DOI: 10.3934/amc.2012.6.229
  • Peer Reviewed
• [Journal Article] Classification of self-dual codes of length 36
  • Author(s): M.Harada, A.Munemasa
  • Journal Title: Advances Math.Communications Volume: (掲載決定)
  • Peer Reviewed
• [Presentation] Magma へ貢献できること (2012)
  • Author(s): 原田 昌晃
  • Organizer: Magmaで開く数学の世界
  • Place of Presentation: 高知大学
• [Presentation] Unimodular lattices with long shadows (2011)
  • Author(s): 原田昌晃
  • Organizer: 離散数理構造とその応用
  • Place of Presentation: 名古屋大学
  • Year and Date: 2011-11-18
• [Presentation] Frames of the Leech lattice (2011)
  • Author(s): 宗政昭弘
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 上海交通大学
  • Year and Date: 2011-09-15
• [Presentation] Self-dual code とその周辺
  • Author(s): 原田昌晃
  • Organizer: 日本数学会 2013 年度秋季総合分科会
  • Place of Presentation: 愛媛大学
  • Invited