Trifferent codes with small lengths
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909498217594880 |
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| author | Kurz, Sascha |
| author_facet | Kurz, Sascha |
| contents | A code $C \subseteq \{0, 1, 2\}^n$ of length $n$ is called trifferent if for any three distinct elements of $C$ there exists a coordinate in which they all differ. By $T(n)$ we denote the maximum cardinality of trifferent codes with length. $T(5)=10$ and $T(6)=13$ were recently determined. Here we determine $T(7)=16$, $T(8)=20$, and $T(9)=27$. For the latter case $n=9$ there also exist linear codes attaining the maximum possible cardinality $27$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_13563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trifferent codes with small lengths Kurz, Sascha Combinatorics Discrete Mathematics 68R05, 68Q17 A code $C \subseteq \{0, 1, 2\}^n$ of length $n$ is called trifferent if for any three distinct elements of $C$ there exists a coordinate in which they all differ. By $T(n)$ we denote the maximum cardinality of trifferent codes with length. $T(5)=10$ and $T(6)=13$ were recently determined. Here we determine $T(7)=16$, $T(8)=20$, and $T(9)=27$. For the latter case $n=9$ there also exist linear codes attaining the maximum possible cardinality $27$. |
| title | Trifferent codes with small lengths |
| topic | Combinatorics Discrete Mathematics 68R05, 68Q17 |
| url | https://arxiv.org/abs/2310.13563 |