English

$t$-Balanced Codes with the Kendall-$\tau$ Metric

Combinatorics 2024-05-24 v1 Information Theory math.IT

Abstract

We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-τ\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 tt-balanced codes in the Kendall-τ\tau metric. The results are based on novel arguments that shed new light on the structure of the Kendall-τ\tau metric space.

Keywords

Cite

@article{arxiv.2405.14228,
  title  = {$t$-Balanced Codes with the Kendall-$\tau$ Metric},
  author = {Benjamin Jany and Alberto Ravagnani},
  journal= {arXiv preprint arXiv:2405.14228},
  year   = {2024}
}
R2 v1 2026-06-28T16:36:42.545Z