Abstract This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length.

中文翻译：

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BAD校正码基数的数论公式及渐近最优性

摘要 本文从外尔群的角度提出了平衡相邻删除的一类非线性纠错码的基数公式，它是作为标准删除的扩展提供的。此外，我们表明基数在任何单个 BAD 校正码上都是近似最优的。换句话说，对于足够大的长度，代码的基数与最大基数BAD校正码的基数之比收敛到1。