标题： $t$- 带有Kendall-$τ$度量的平衡码 显示英文标题

标题： $t$-Balanced Codes with the Kendall-$τ$ Metric

摘要： 我们研究了具有Kendall-$\tau$度量的纠错码的最大基数和数学结构。 我们建立了具有指定最小距离的码的基数的平均界，讨论了其紧性，并表征了达到该界的码。 这导致在Kendall-$\tau$度量中引入了$t$-平衡码族。 这些结果基于新的论点，为Kendall-$\tau$度量空间的结构提供了新的见解。 显示英文摘要

摘要： 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.