Ken Saito

Ken Saito


Research Interests

    I am interested in Algebraic Combinatorics, Coding Theory, Error-Correcting Codes, Self-Dual Codes, Combinatorial Design Theory and so on.

Algebraic Coding Theory

    Claude Shannon's paper "A Mathematical Theory of Communication" [1], written in 1948, started the discipline in electrical engineering called information theory, and also the branch of it called error-correcting codes.
    It is unknown whether a binary doubly-even [72,36,16] code exists or not.   This is one of the long-standing open problems suggested by Sloane [2] in 1973.

  1. C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27, (1948), 379-423, 623-656.
  2. N. J. A. Sloane, Is there a (72,36) d=16 self-dual code?, IEEE Trans. Information Theory IT-19, (1973), no. 2, 251.

Curriculum Vitae


  • Birth: May 3, 1991 at Tsuruoka (Yamagata pref.), Japan


  • April, 2016 - Present: Graduate School of Information Sciences, Tohoku University


  • Master: Graduate School of Information Sciences, Tohoku University, March, 2016 (adviser: Masaaki Harada)
  • Bachelor: Department of Mathematical Sciences, Faculty of Science, Yamagata University, March, 2014


Publications (Submitted)

  1. Binary linear complementary dual codes (with Masaaki Harada), submitted to Cryptography and Communications (2018.2.20), [arXiv: 1802.06985].
  2. Self-dual additive F4-codes of lengths up to 40 represented by circulant graphs, submitted to Advances in Mathematics of Communications (2017.1.21).

Publications (In Press)

Publications (In Print)

  1. Singly even self-dual codes constructed from Hadamard matrices of order 28 (with Masaaki Harada), Australasian Journal of Combinatorics 70 (2018), 288-296, (published: 2017.12.13).
  2. On the classification of Z4-codes (with Makoto Araya, Masaaki Harada and Hiroki Ito), Advances in Mathematics of Communications 11 (2017), 747-756, (published: 2017.11.30).


  1. On binary codes with complementary dual, 「The 5th Taiwan-Japan Conference on Combinatorics and its Applications」, National Taiwan Normal University, 2018年3月29日
  2. Singly even self-dual codes constructed from Hadamard matrices, 「研究集会『実験計画法と符号および関連する組合せ構造』2017」, 湯河原温泉 おんやど恵, 2017年11月24日
  3. 単純グラフから構成される符号の分類, 「日本数学会2017年度秋季総合分科会」, 山形大学, 2017年9月13日
  4. On additive F4-codes constructed from graphs, 「第13回組合せ論若手研究集会」, 慶應義塾大学(矢上キャンパス), 2017年3月1日
  5. Additive F4-codes constructed by circulant graphs, 「研究集会「実験計画法と符号および関連する組合せ構造」」, 秋保リゾートホテルクレセント, 2016年11月29日
  6. 巡回行列から構成される4元体上の符号の分類, 「離散数理セミナー」, 山形大学(理学部・大学院理工学研究科), 2016年6月9日
  7. Circulant graph code の性質と分類, 「ミニ集会「代数的組合せ論とその周辺」」, 東北大学(情報科学研究科), 2016年3月8日

Master's Thesis

    位数4の有限体上の additive code について, 修士論文, 東北大学, 2016.




  • Classification of bordered circulant graph F4-codes
  • Classification of additive circulant graph F4-codes
  • Code Tables: Bounds on the parameters of various types of codes
  • Database of self-dual codes
  • E-mail

      kensaito "at"

    Last Update: April 4, 2018