Binary periodic synchronizing sequences

Binary Periodic Synchronizing Sequences

In this article, we consider words over f0; 1g of length l 2. The autodistance of such a word is the lowest among the Hamming distances between the word and its images by circular permutations other than identity; the word’s reverse autodistance is the highest among these distances. For each l 2, we study the words of length l whose autodistance and reverse autodistance are close to l=2 (we cal...

Recognition of Patterns in Periodic Binary Sequences

When humans are presented with information, they tend to search for structure in the information-to encode it, to organize it, to look for regularities. The existence of this structure-seeking behavior can be seen in the behavior of subjects predicting a random sequence of binary events and in the behavior of subjects predicting more highly structured sequences. (A random sequence is a colloqui...

On Aperiodic and Periodic Complementary Binary Sequences

We give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bömer and Antweiler [4] can be filled.

Periodic complementary sets of binary sequences

Let P CS N p denote a set of p binary sequences of length N such that the sum of their periodic auto-correlation functions is a δ-function. In the 1990, Bömer and Antweiler addressed the problem of constructing P CS N p. They presented a table covering the range p ≤ 12, N ≤ 50 and showing in which cases it was known at that time whether P CS N p exist, do not exist, or the question of existence...

Homing and Synchronizing Sequences