$t$-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- 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 -balanced codes in the Kendall- metric. The results are based on novel arguments that shed new light on the structure of the Kendall- 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}
}