Constructions for higher dimensional perfect multifactors

Abstract

Abstract. A d-dimensional Perfect Factor is a collection of periodic arrays in which every k-ary (n 1 ×· · ·×n d ) matrix appears appears exactly once (periodically). The one dimensional case, with a collection of size one, is known as a De Bruijn cycle. The 1-and 2-dimensional versions have proven highly applicable in areas such as coding, communications, and location sensing. Here we focus on results in higher dimensions for factors with each n i = 2.

3D Reconstruction Method Based on Binary coded Pattern

“…Therefore, pattern coding methods, such as the pseudorandom, M-array, perfect map, and De Bruijn methods, have been investigated for a long time in order to facilitate the pattern decoding [14,16]. These pattern encoding methods create symbols for uniqueness within a specific range.…”