鹿児島大学 · 理工学研究科 · 教授

研究关键词algebraic-geometric codes・affine variety codes・Reed-Muller codes・quasi-cyclic codes・discrete Fourier transforms・self-dual codes・Chinese remainder theorem・error-correcting codes

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• Norifumi Ojiro, Hajime Matsui . Minimum weights of codes over integer residue rings generated by Kronecker products of certain integer matrices . Advances in Mathematics of Communicati2024 · 担当区分： 最終著者 記述言語： 英語 掲載種別： 研究論文（学術雑誌） DOI： 10.3934/amc.2024030
• Matsui H. . An Algorithm for Finding Self-Orthogonal and Self-Dual Codes Over Gaussian and Eisenstein Integer Residue Rings Via Chinese Remainder Theorem . IEEE Access112023 · 担当区分： 筆頭著者, 責任著者 記述言語： 英語 掲載種別： 研究論文（学術雑誌） 出版者・発行元： IEEE Access A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define the dual codes for the codes over the Gaussian and Eisenstein integer residue rings, and consider the construction of the self-dual codes. Because, in the Gaussian and Eisenstein integer rings, the uniqueness of the prime element decomposition holds in the same way as the one-variable polynomial rings over finite fields and the rational integer ring, we provide an efficient construction method for self-dual code generator matrices using that of moduli. As numerical examples, for Gaussian and Eisenstein integer rings, we enumerate and construct the self-dual codes for the actual moduli when the size of the generator matrices is two. DOI： 10.1109/access.2023.3253774 Scopus
• Norifumi Ojiro, Kakeru Kaneko, Hajime Matsui . An efficient algorithm for constructing reversible quasi-cyclic codes via Chinese remainder theorem . Finite Fields and Their Application2023 · 担当区分： 最終著者 記述言語： 英語 掲載種別： 研究論文（学術雑誌） 出版者・発行元： Finite Fields and their Applications Regarding quasi-cyclic codes as certain polynomial matrices, we show that all reversible quasi-cyclic codes are decomposed into reversible linear codes of shorter lengths corresponding to the coprime divisors of the polynomials with the form of one minus x to the power of m. This decomposition brings us an efficient method to construct reversible quasi-cyclic codes. We also investigate the reversibility and the self-duality of the linear codes corresponding to the coprime divisors of the polynomials. Specializing to the cases where the number of cyclic sections is not more than two, we give necessary and sufficient conditions for the divisors of the polynomials for which the self-dual codes are reversible and the reversible codes of half-length-dimension are self-dual. Our theorems are utilized to search reversible self-dual quasi-cyclic codes with two cyclic sections over binary and quaternary fields of lengths up to seventy and thirty-six, respectively, together with the maximums of their minimum weights. DOI： 10.1016/j.ffa.2023.102204 DOI： 10.1016/j.ffa.2023.102204 Scopus
• Norifumi Ojiro, Hajime Matsui . Construction of reversible integer codes with large moduli via Chinese remainder theorem . International Symposium on Information Theory and Its Applica2022 · 担当区分： 最終著者 記述言語： 英語 掲載種別： 研究論文（国際会議プロシーディングス） The codes over rational integer residue rings are called integer codes. In this paper, we give a necessary and sufficient condition concerning the generator matrices when integer codes are to be reversible and show that their reversibility is preserved from the decomposition of integer codes by Chinese remainder theorem. This brings an efficient method for constructing of reversible integer codes with large moduli. Using this method, we enumerate reversible self-dual integer codes of length 3,4 with various moduli. Further, we claim that reversible and self-dual integer codes produce reversible and unimodular lattices, respectively. As a result, we see that the extended binary Hamming code produces the even unimodular lattice of rank 8 and in particular this lattice is reversible, and furthermore the lattice induces an extremal Type II integer code of length 8 with modulus 4.

• 情報活用2024 · 2024年4月 - 現在 機関名： 鹿児島大学
• 情報科学入門2024 · 2024年4月 - 現在 機関名： 鹿児島大学
• 誤り訂正符号と多値論理関数との離散フーリエ変換による関係性解明2019 · 担当区分： 研究代表者 配分額： 6370000円 （ 直接経費： 4900000円 、 間接経費： 1470000円 ） 1．拡大有限体上の巡回符号から得られる準巡回（QC）符号の生成多項式行列を求めた．また，生成多項式行列Gから定まるQC符号Qについて，Qが拡大有限体上のある巡回符号から得られるためのGの必要十分条件を求めた．応用として，拡大有限体上の巡回符号から得られるQC符号が反転不変であるための巡回符号のスペクトラムについての必要十分条件を求めた． 2．一般のQC符号について研究を行い，反転不変符号，自己直交符号，および自己双対符号の生成多項式行列を決定した．本研究の結果を利用した計算機探索によって，最小距離の上限を達成する自己直交である様々な反転不変QC符号を発見することができた．
• 勉強するのはなんのため？ワクワク未来教室『CDは傷に弱い？！』2016 · 中日新聞 中日こどもウイークリー 248号，p.10 2016年4月

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