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$t$-Balanced Codes with the Kendall-$τ$ Metric
Published 23 May 2024 in math.CO, cs.IT, and math.IT | (2405.14228v1)
Abstract: 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.
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