| Presentation | 2024-01-18 On Hadamard-type Matrices of Odd Order over Finite Fields Iori Kodama, Tetsuya Kojima, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Hadamard-type Matrix on finite fields has been proposed. This matrix is defined as a square matrix on GF(p), where each row is orthogonal to each other, and the norm of each row is equal to the order n of the matrix. Previous works by the authors have shown how to generate Hadamard-type matrices of cyclic type, where the matrix components are cyclic. It has been also shown that the order of the matrix is limited to the quadratic residue of p. In this study, we prove that the order of any Hadamard-type matrix of odd order is limited to the quadratic residue of p. We also discuss how to extend these matrices to higher orders. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Hadamard-type matrix / finite field / quadratic residue |
| Paper # | IT2023-40,SIP2023-73,RCS2023-215 |
| Date of Issue | 2024-01-11 (IT, SIP, RCS) |
| Conference Information | |
| Committee | SIP / IT / RCS |
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| Conference Date | 2024/1/18(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Takayuki Nakachi(Ryukyu Univ.) / Tetsuya Kojima(Tokyo Kosen) / Kenichi Higuchi(Tokyo Univ. of Science) |
| Vice Chair | Koichi Ichige(Yokohama National Univ.) / Kiyoshi Nishikawa(okyo Metropolitan Univ.) / Yasuyuki Nogami(Okayama Univ.) / Fumihide Kojima(NICT) / Osamu Muta(Kyushu Univ.) / Naoto Ishii(NEC) |
| Secretary | Koichi Ichige(Chiba Univ.) / Kiyoshi Nishikawa(Kogakuin Univ.) / Yasuyuki Nogami(Waseda Univ.) / Fumihide Kojima(Nagaoka Univ. of Tech.) / Osamu Muta(Univ. of Electro-Comm) / Naoto Ishii(Sharp) |
| Assistant | Taichi Yoshida(UEC) / Sayaka Shiota(Tokyo Metropolitan Univ.) / Tetsunao Matsuta(Saitamai Univ.) / Masashi Iwabuchi(NTT) / Issei Kanno(KDDI Research) / Yuyuan Chang(Tokyo Inst. of Tech) / Kazuki Maruta(Tokyo Univ. of Science) / Kiichi Tateishi(NTT Docomo) |
| Paper Information | |
| Registration To | Technical Committee on Signal Processing / Technical Committee on Information Theory / Technical Committee on Radio Communication Systems |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On Hadamard-type Matrices of Odd Order over Finite Fields |
| Sub Title (in English) | |
| Keyword(1) | Hadamard-type matrix |
| Keyword(2) | finite field |
| Keyword(3) | quadratic residue |
| 1st Author's Name | Iori Kodama |
| 1st Author's Affiliation | National Institute of Technology, Tokyo College(NIT, Tokyo College) |
| 2nd Author's Name | Tetsuya Kojima |
| 2nd Author's Affiliation | National Institute of Technology, Tokyo College(NIT, Tokyo College) |
| Date | 2024-01-18 |
| Paper # | IT2023-40,SIP2023-73,RCS2023-215 |
| Volume (vol) | vol.123 |
| Number (no) | IT-338,SIP-339,RCS-340 |
| Page | pp.pp.57-61(IT), pp.57-61(SIP), pp.57-61(RCS), |
| #Pages | 5 |
| Date of Issue | 2024-01-11 (IT, SIP, RCS) |