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.

Personal

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

Position

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

Education

• 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).

Talks

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.

Links

• Graduate School of Information Sciences, Tohoku University
• Combinatorics Seminar

Databases

E-mail

kensaito "at" ims.is.tohoku.ac.jp