| Presentation | 2019-09-06 [Invited Talk] Hadamard-type Matrices on Finite Fields and Some Open Problems Tetsuya Kojima, |
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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. In this work, we consider the similar matrix on finite field $GF(p)$ where $p$ is an odd prime. In such a matrix, every component is one of the integers on $GF(p) ￥backslash ￥{0￥}$, that is, $￥{ 1, 2, ￥ldots, p-1￥}$. Any additions and multiplications should be executed under modulo $p$. In this talk, the methods to generate such matrices and some properties of them are chronologically introduced. Some open problems at this moment are also included. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Hadamard-type matrix / finite field / cyclic group / multiplicative inverse / complete complementary code |
| Paper # | IT2019-31 |
| Date of Issue | 2019-08-30 (IT) |
| Conference Information | |
| Committee | IT |
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| Conference Date | 2019/9/6(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Yufuin Kenshujo, Nippon Bunri University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | error correcting codes, general |
| Chair | Jun Muramatsu(NTT) |
| Vice Chair | Tadashi Wadayama(Nagoya Inst. of Tech.) |
| Secretary | Tadashi Wadayama(Saga Univ.) |
| Assistant | Hideki Yagi(UEC) |
| Paper Information | |
| Registration To | Technical Committee on Information Theory |
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| Language | ENG-JTITLE |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | [Invited Talk] Hadamard-type Matrices on Finite Fields and Some Open Problems |
| Sub Title (in English) | |
| Keyword(1) | Hadamard-type matrix |
| Keyword(2) | finite field |
| Keyword(3) | cyclic group |
| Keyword(4) | multiplicative inverse |
| Keyword(5) | complete complementary code |
| 1st Author's Name | Tetsuya Kojima |
| 1st Author's Affiliation | National Institute of Technology, Tokyo College(NIT, Tokyo College) |
| Date | 2019-09-06 |
| Paper # | IT2019-31 |
| Volume (vol) | vol.119 |
| Number (no) | IT-198 |
| Page | pp.pp.29-34(IT), |
| #Pages | 6 |
| Date of Issue | 2019-08-30 (IT) |