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.
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Jany et al. (2024) studied this question.
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