In this paper we study the problem of finding maximally sized subsets of binary strings (codes) of equal length that are immune to a given number r of repetitions, in the sense that no two strings in the code can give rise to the same string after r repetitions. We propose explicit number theoretic constructions of such subsets. In the case of r = 1 repetition, the proposed construction is asym...

Length estimation of three dimensional digitized curves is considered. Three dimensional 26-directional chain code representation is assumed. Recent results on 3 ? D Euclidean Distance Maps are inapplicable to optimal 3 ? D length estimation. To support optimal design of three dimensional length estimators, chain code probabilities in three dimensional chain encoded digital straight lines are d...

We consider the problem of constructing binary codes to recover from k–bit deletions with efficient encoding/decoding, for a fixed k. The single deletion case is well understood, with the VarshamovTenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with ≈ 2n/n codewords of length n, i.e., at most logn bits of redundancy. However, even for the case of two deletion...