Comprehensive research on algebraic coding theory

• Project/Area Number: 15H03633
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tohoku University
• Principal Investigator: Harada Masaaki 東北大学, 情報科学研究科, 教授 (90292408)
• Co-Investigator(Kenkyū-buntansha): 宗政 昭弘 東北大学, 情報科学研究科, 教授 (50219862)
• Research Collaborator: MIYAMOTO masahiko ; KITAZUME masaaki ; WADAYAMA tadashi ; ARAYA makoto ; BETSUMIYA koichi ; OURA manabu ; SHIMAKURA hiroki ; TANAKA hajime ; SUDA sho
• Project Period (FY): 2015-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥14,950,000 (Direct Cost: ¥11,500,000、Indirect Cost: ¥3,450,000); Fiscal Year 2018: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2017: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
• 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 / 離散数学 / 離散構造

Outline of Final Research Achievements

In this research project, I studied algebraic coding theory, especially, self-dual codes. I obtained results about the existence and the nonexistence of singly even self-dual codes.
Moreover, I obtained results about linear complementary dual codes. These codes are a class of linear codes which are related to cryptography.

Academic Significance and Societal Importance of the Research Achievements

代数的符号理論は、誤りの発生する可能性のある通信路の数理モデルにおける符号化の部分に現れる組合せ構造である符号を代数的な立場で研究を行った。組合せ構造の研究において、基本的な課題である良い符号の構成と分類についての成果を得ることが出来たことが本研究における学術的な意義である。また、暗号理論との関連のある符号についての研究成果も得ることが出来た。

Research Products

• [Int'l Joint Research] University of Victoria(カナダ)
• [Int'l Joint Research] Konstantin Preslavski Univ. Shumen(ブルガリア)
• [Int'l Joint Research] Michigan Technological University(米国)
• [Int'l Joint Research] University of Victoria(カナダ)
• [Int'l Joint Research] Michigan Technological University(米国)
• [Int'l Joint Research] University of Victoria(カナダ)
• [Int'l Joint Research] Michigan Technological University(米国)
• [Int'l Joint Research] University of Victoria(カナダ)
• [Int'l Joint Research] Universitat Erlangen-Nurnberg(ドイツ)
• [Journal Article] New doubly even self-dual codes having minimum weight 20 (2019)
  • Author(s): Masaaki Harada
  • Journal Title: Advances Math. Communications Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] On extremal double circulant self-dual codes of lengths 90-96 (2019)
  • Author(s): T. Aaron Gulliver and Masaaki Harada
  • Journal Title: Applicable Algebra in Eng. Communi. Comput. Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Binary linear complementary dual codes (2019)
  • Author(s): Masaaki Harada and Ken Saito
  • Journal Title: Cryptography and Communications Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] On the classification of linear complementary dual codes (2019)
  • Author(s): Makoto Araya and Masaaki Harada
  • Journal Title: Discrete Math. Volume: 342 Issue: 1 Pages: 270-278
  • DOI: 10.1016/j.disc.2018.09.034
  • Peer Reviewed / Open Access
• [Journal Article] New extremal singly even self-dual codes of lengths 64 and 66 (2018)
  • Author(s): Damyan Anev, Masaaki Harada and Nikolay Yankov
  • Journal Title: J. Algebra Comb. Discrete Struct. Appl. Volume: 5 Issue: 3 Pages: 143-151
  • DOI: 10.13069/jacodesmath.458601
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Some Restrictions on Weight Enumerators of Singly Even Self-Dual Codes II (2018)
  • Author(s): Masaaki Harada and Akihiro Munemasa
  • Journal Title: Interdisciplinary Information Sciences Volume: 24 Issue: 1 Pages: 77-85
  • DOI: 10.4036/iis.2017.R.03
  • NAID: 130007412755
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access
• [Journal Article] New quantum codes constructed from some self-dual additive F4-codes (2018)
  • Author(s): Masaaki Harada
  • Journal Title: Information Processing Letters Volume: 138 Pages: 35-38
  • DOI: 10.1016/j.ipl.2018.05.008
  • Peer Reviewed / Open Access
• [Journal Article] Singly even self-dual codes of length 24k+10 and minimum weight 4k+2 (2018)
  • Author(s): M. Harada
  • Journal Title: Cryptography and Communications Volume: 印刷中
  • Peer Reviewed / Open Access
• [Journal Article] Some restrictions on weight enumerators of singly even self-dual codes II (2018)
  • Author(s): M. Harada and A. Munemasa
  • Journal Title: Interdiscip. Inform. Sci. Volume: 印刷中
  • NAID: 130007412755
  • Peer Reviewed / Open Access
• [Journal Article] Binary extremal self-dual codes of length 60 and related codes (2018)
  • Author(s): Harada Masaaki
  • Journal Title: Designs, Codes and Cryptogr. Volume: 86 Issue: 5 Pages: 1085-1094
  • DOI: 10.1007/s10623-017-0380-2
  • Peer Reviewed / Open Access
• [Journal Article] Nonexistence of certain singly even self-dual codes with minimal shadow (2018)
  • Author(s): S. Bouyuklieva, M. Harada and A. Munemasa
  • Journal Title: Electronic J. Combin. Volume: 25
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$ (2018)
  • Author(s): Araya Makoto、Harada Masaaki、Suzuki Yuichi
  • Journal Title: J. Algebra Comb. Discrete Struct. Appl. Volume: 5 Pages: 1-4
  • DOI: 10.13069/jacodesmath.327391
  • Peer Reviewed / Open Access
• [Journal Article] Singly even self-dual codes constructed from Hadamard matrices of order 28 (2018)
  • Author(s): M. Harada and K. Saito
  • Journal Title: Australasian J. Combin. Volume: 70 Pages: 288-296
  • Peer Reviewed / Open Access
• [Journal Article] On the classification of Z4-codes (2017)
  • Author(s): Araya Makoto、Harada Masaaki、Ito Hiroki、Saito Ken
  • Journal Title: Advances Math. Communications Volume: 11 Issue: 4 Pages: 747-756
  • DOI: 10.3934/amc.2017054
  • Peer Reviewed / Open Access
• [Journal Article] On the performance of optimal double circulant even codes (2017)
  • Author(s): Gulliver T. Aaron、Harada Masaaki
  • Journal Title: Advances Math. Communications Volume: 11 Issue: 4 Pages: 767-775
  • DOI: 10.3934/amc.2017056
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Performance of ternary double circulant, double twistulant, and self-dual codes (2017)
  • Author(s): Gulliver T. Aaron、Harada Masaaki
  • Journal Title: Applicable Algebra in Eng. Communi. Comput. Volume: 28 Issue: 5 Pages: 409-424
  • DOI: 10.1007/s00200-017-0312-4
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On s -extremal singly even self-dual [24 k + 8,12 k + 4,4 k + 2] codes (2017)
  • Author(s): Harada Masaaki、Munemasa Akihiro
  • Journal Title: Finite Fields and Their Applications Volume: 48 Pages: 306-317
  • DOI: 10.1016/j.ffa.2017.08.008
  • Peer Reviewed / Open Access
• [Journal Article] Self-Dual Codes and the Nonexistence of a Quasi-Symmetric 2-(37,9,8) Design with Intersection Numbers 1 and 3 (2017)
  • Author(s): Harada Masaaki、Munemasa Akihiro、Tonchev Vladimir D.
  • Journal Title: J. Combin. Designs Volume: 25 Issue: 10 Pages: 469-476
  • DOI: 10.1002/jcd.21556
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Extremal Type II Z4-codes constructed from binary doubly even self-dual codes of length 40 (2017)
  • Author(s): Harada Masaaki
  • Journal Title: Discrete Math Volume: 340 Issue: 10 Pages: 2466-2468
  • DOI: 10.1016/j.disc.2017.06.009
  • Peer Reviewed
• [Journal Article] New self-dual additive F4-codes constructed from circulant graphs (2017)
  • Author(s): Masaaki Harada and Markus Grassl
  • Journal Title: Discrete Math. Volume: 340 Issue: 3 Pages: 399-403
  • DOI: 10.1016/j.disc.2016.08.023
  • 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: Australasian J. Combin. Volume: 65 Pages: 71-83
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The weight distribution of the self-dual [128,64] polarity design code (2016)
  • Author(s): Masaaki Harada, Ethan Novak and Vladimir D. Tonchev
  • Journal Title: Advances Math. Communications Volume: 42 Issue: 3 Pages: 57-66
  • DOI: 10.3934/amc.2016032
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The weight distribution of the self-dual [128, 64] polarity design code (2016)
  • Author(s): Masaaki Harada, Ethan Novak and Vladimir D. Tonchev
  • Journal Title: Advances Math. Communications Volume: -
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] On linear complementary dual codes (2019)
  • Author(s): 原田昌晃
  • Organizer: 組合せ論的符号理論
• [Presentation] On the nonexistence of certain extremal doubly even self-dual codes (2016)
  • Author(s): 原田昌晃
  • Organizer: 離散数学とその応用研究集会２０１６
  • Place of Presentation: 高城コミュニティセンター(宮城県宮城郡松島町)
  • Year and Date: 2016-08-21
• [Remarks] 原田昌晃研究室
  • URL: http://www.math.is.tohoku.ac.jp/~mharada/