A binary code is said to be an \((s,\ell)\)-separating code if for any two disjoint sets of its codewords of cardinalities at most \(s\) and \(\ell\) respectively, there exists a coordinate in which all words of the first set have symbol 0 while all words of the second have 1. If, moreover, for any two sets there exists a second coordinate in which all words of the first set have 1 and all words of the second have 0, then such a code is called an \((s,\ell)\)-completely separating code. We improve upper bounds on the rate of separating and completely separating codes.

中文翻译：

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提高分离和完全分离代码率的上限

如果对于任意两个不相交的基数码字集至多为\ ( s\ )和一个坐标，其中第一组的所有单词都具有符号 0，而第二组的所有单词都具有 1。此外，如果对于任何两个集合存在第二个坐标，其中第一组的所有单词都具有 1，而第二个有 0，那么这样的代码称为\((s,\ell)\) -完全分离代码。我们提高了代码分离和完全分离率的上限。