$t$-Balanced Codes with the Kendall-$\tau$ Metric
<|reference_start|>$t$-Balanced Codes with the Kendall-$\tau$ Metric: We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-$\tau$ 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-$\tau$ metric. The results are based on novel arguments that shed new light on the structure of the Kendall-$\tau$ metric space.<|reference_end|>
@article{jany2024$t$-balanced,
    title={$t$-Balanced Codes with the Kendall-$\tau$ Metric},
    author={Benjamin Jany and Alberto Ravagnani},
    journal={arXiv preprint arXiv:2405.14228},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14228},
    primaryClass={math.CO cs.IT math.IT}
}