| Presentation | 2023-05-12 Some Remarks on Hadamard-type Matrices over Residue Class Rings or Finite Fields Tetsuya Kojima, Iori Kodama, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Hadamard matrix is defined as a square matrix where any components are $-1$ or $+1$, and where any pairs of rows are mutually orthogonal. On the other hand, Hadamard-type matrices on finite field have been proposed. This matrix is a similar matrix as a binary Hadamard matrix, but has multi-valued components on finite fields. To be more specific, we consider $n times n$ matrices that have their elements on the given finite fields, and satisfy $HH^{T} equiv nI$, where $I$ is an identity matrix. Recently, the authors have discovered a special type of Hadamard-type matrices called cyclic Hadamard-type matrices on finite fields, and proposed its generation method. In this paper, we introduce some properties of such cyclic Hadamard-type matrices. For example, these matrices has non-zero elements on finite fields as well as zeroes. In addition, it is pointed out that these matrices can be generated not only on finite fields, but also on residue class rings based upon non-prime. It is also discussed that involutory matrices can be obtained by Hadamard-type matrices. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Hadamard-type matrix / cyclic Hadamard-type matrix / finite field / residue class ring / involutory matrix |
| Paper # | IT2023-13,EMM2023-13 |
| Date of Issue | 2023-05-04 (IT, EMM) |
| Conference Information | |
| Committee | EMM / IT |
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| Conference Date | 2023/5/11(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Rakuyu Kaikan (Kyoto Univ. Yoshida-South Campus) |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Information Security, Information Theory, Information Hiding, etc. |
| Chair | Ryoichi Nishimura(NICT) / Tetsuya Kojima(Tokyo Kosen) |
| Vice Chair | Kotaro Sonoda(Nagasaki Univ.) / Masatsugu Ichino(Univ. of Electro-Comm.) / Yasuyuki Nogami(Okayama Univ.) |
| Secretary | Kotaro Sonoda(Kaishi Professional Univ.) / Masatsugu Ichino(Chiba Univ.) / Yasuyuki Nogami(Saitamai Univ.) |
| Assistant | Tomoko Kajiyama(Hiroshima City Univ.) / Shieyuki Sakazawa(Osaka Inst. of Tech.) / Takayuki Nozaki(Yamaguchi Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Enriched MultiMedia / Technical Committee on Information Theory |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Some Remarks on Hadamard-type Matrices over Residue Class Rings or Finite Fields |
| Sub Title (in English) | |
| Keyword(1) | Hadamard-type matrix |
| Keyword(2) | cyclic Hadamard-type matrix |
| Keyword(3) | finite field |
| Keyword(4) | residue class ring |
| Keyword(5) | involutory matrix |
| 1st Author's Name | Tetsuya Kojima |
| 1st Author's Affiliation | National Institute of Technology, Tokyo College(NIT, Tokyo College) |
| 2nd Author's Name | Iori Kodama |
| 2nd Author's Affiliation | National Institute of Technology, Tokyo College(NIT, Tokyo College) |
| Date | 2023-05-12 |
| Paper # | IT2023-13,EMM2023-13 |
| Volume (vol) | vol.123 |
| Number (no) | IT-14,EMM-15 |
| Page | pp.pp.67-72(IT), pp.67-72(EMM), |
| #Pages | 6 |
| Date of Issue | 2023-05-04 (IT, EMM) |