A code is a subset of the vertex set of a Hamming graph. The set of s-neighbours of a code is the set of all vertices at Hamming distance s from their nearest codeword. A code C is s-elusive if there exists a distinct code \(C'\) that is equivalent to C under the full automorphism group of the Hamming graph such that C and \(C'\) have the same set of s-neighbours. We show that the minimum distance of an s-elusive code is at most \(2s+2\), and that an s-elusive code with minimum distance at least \(2s+1\) gives rise to a q-ary t-design with certain parameters. This leads to the construction of: an infinite family of 1-elusive and completely transitive codes, an infinite family of 2-elusive codes, and a single example of a 3-elusive code. Answers to several open questions on elusive codes are also provided.

甲代码是顶点集的一个子集汉明图。该组的小号-neighbours的代码是定在汉明距离所有顶点的小号，从他们最近的码字。A码Ç是小号-难以捉摸如果存在一个不同的码\（C“\） ，它等效于Ç的全自同构组的汉明图的下使得Ç和\（C” \）具有同一组的小号-邻居。我们证明s-难以捉摸的代码的最小距离最大为\（2s + 2 \），并且最小距离至少为\（2s + 1 \）的s-难以捉摸的代码会产生带有某些参数的q -ary t-设计。这导致了以下内容的构造：无限的1难以捉摸的代码和完全可及的代码，无限的2易捉摸的代码家族，以及3易捉摸的代码的单个示例。还提供了对一些难以捉摸的代码的开放式问题的答案。