| Presentation | 2020-12-03 Hamming Distance Enumerators for Number Theoretic Codes Takayuki Nozaki, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The number theoretic codes are defined by single or multiple congruences and are used for correcting insertion and deletion errors. Since the number theoretic codes are generally non-linear, the analysis method for such codes is not enough established. Hamming distance enumerator of a code is a unary polynomial whose $i$th coefficient gives the fraction of the pair of codewords with Hamming distance $i$. Hamming distance enumerator gives the maximum likelihood decoding error probability of the code through symbol substitution channel. This report presents the Hamming distance enumerators for the number theoretic codes. Moreover, as an example, we derive the Hamming distance enumerator for the Varshamov-Tenengolts (VT) codes. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Number theoretic code / Hamming distance enumerator / non-linear code / VT code |
| Paper # | IT2020-48 |
| Date of Issue | 2020-11-24 (IT) |
| Conference Information | |
| Committee | IT |
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| Conference Date | 2020/12/1(3days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Lectures for Young Researchers, General |
| Chair | Tadashi Wadayama(Nagoya Inst. of Tech.) |
| Vice Chair | Tetsuya Kojima(Tokyo Kosen) |
| Secretary | Tetsuya Kojima(Yamaguchi Univ.) |
| Assistant | Takahiro Ohta(Senshu Univ.) |
| Paper Information | |
| Registration To | 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) | Hamming Distance Enumerators for Number Theoretic Codes |
| Sub Title (in English) | |
| Keyword(1) | Number theoretic code |
| Keyword(2) | Hamming distance enumerator |
| Keyword(3) | non-linear code |
| Keyword(4) | VT code |
| 1st Author's Name | Takayuki Nozaki |
| 1st Author's Affiliation | Yamaguchi University(Yamaguchi Univ) |
| Date | 2020-12-03 |
| Paper # | IT2020-48 |
| Volume (vol) | vol.120 |
| Number (no) | IT-268 |
| Page | pp.pp.134-139(IT), |
| #Pages | 6 |
| Date of Issue | 2020-11-24 (IT) |