On binary sequences

On Jacobsthal Binary Sequences

S. Magliveras and W. Wei∗, Florida Atlantic University Let Σ = {0, 1} be the binary alphabet, and A = {0, 01, 11} the set of three strings 0, 01, 11 over Σ. Let A∗ denote the Kleene closure of A, and Z the set of positive integers. A sequence in A∗ is called a Jacobsthal binary sequence. The number of Jacobsthal binary sequences of length n ∈ Z is the n Jacobsthal number. Let k ∈ Z, 1 ≤ k ≤ n. ...

On p-pseudorandom binary sequences

where the maximum is taken over all a, b, t ∈ IN such that 1 ≤ a ≤ a + (t − 1)b ≤ N , while the correlation measure of order k of EN is defined as Research of the second author is partially supported by Hungarian National Foundation for Scientific Research, Grant no. T043623. This paper was written while the second author was visiting the Institut de Mathématiques de Luminy (UPR 9016 CNRS), Mar...

On The Correlation of Binary Sequences

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.

On the correlation of binary sequences, II

This paper concerns the study of the correlation measures of finite binary sequences, more particularily the dependence of correlation measures of even order and correlation measures of odd order. These results generalize previous results due to Gyarmati [7] and to Anantharam [3] and provide a partial answer to a conjecture due to Mauduit [12]. The last part of the paper concerns the generaliza...