$t$-Balanced Codes with the Kendall-$τ$ Metric
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914808281956352 |
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| author | Jany, Benjamin Ravagnani, Alberto |
| author_facet | Jany, Benjamin Ravagnani, Alberto |
| contents | We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-$τ$ metric. We establish an averaging bound for the cardinality of a code with prescribed minimum distance, discuss its sharpness, and characterize codes attaining it. This leads to introducing the family of $t$-balanced codes in the Kendall-$τ$ metric. The results are based on novel arguments that shed new light on the structure of the Kendall-$τ$ metric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $t$-Balanced Codes with the Kendall-$τ$ Metric Jany, Benjamin Ravagnani, Alberto Combinatorics Information Theory We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-$τ$ metric. We establish an averaging bound for the cardinality of a code with prescribed minimum distance, discuss its sharpness, and characterize codes attaining it. This leads to introducing the family of $t$-balanced codes in the Kendall-$τ$ metric. The results are based on novel arguments that shed new light on the structure of the Kendall-$τ$ metric space. |
| title | $t$-Balanced Codes with the Kendall-$τ$ Metric |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2405.14228 |