A special type of cyclic sequences named adjacency-hopping de Bruijn sequences is introduced in this paper. It is theoretically proved the existence of such sequences, and the number of such sequences is derived. These sequences guarantee that all neighboring codes are different while retaining the uniqueness of subsequences, which is a significant characteristic of original de Bruijn sequences in coding and matching. At last, the adjacency-hopping de Bruijn sequences are applied to structured light coding, and a color fringe pattern coded by such a sequence is presented. In summary, the proposed sequences demonstrate significant advantages in structured light coding by virtue of the uniqueness of subsequences and the adjacency-hopping characteristic, and show potential for extension to other fields with similar requirements of non-repetitive coding and efficient matching.

翻译：本文介绍了一类特殊循环序列——邻跳德布鲁因序列。理论上证明了此类序列的存在性，并推导了其数量。这些序列在保证子序列唯一性的同时，确保所有相邻编码互不相同，而子序列唯一性正是原始德布鲁因序列在编码与匹配中的重要特性。最后，将邻跳德布鲁因序列应用于结构光编码，并给出了由该序列编码的彩色条纹图案。综上，所提出的序列凭借子序列唯一性与邻跳特性，在结构光编码中展现出显著优势，并有望扩展至其他具有非重复编码与高效匹配需求的领域。