مرکز منطقه ای اطلاع رساني علوم و فناوري - On the classification of balanced binary sequences of period <img src="/images/tex/99.gif" alt="2^n-1"> (Corresp.)

Abstract :

Let $U$ be the set of all binary sequences of period $p=2^{n}-1$ containing $(p+1)/2$ ones and $(p-1)/2$ zeros per period. There is a lattice of interesting subsets of $U$ , the smallest of which is the set $PN$ (the maximum-length linear shift register sequences of period $p$ ). In between are sets with the run statistics of $PN$ , with the correlation properties of $PN$ , with the "span- $n$ property" (that every nonzero subseqnonce of length $n$ occurs in each period), and others. Results concerning the interrelationships of these subsets are obtained, examples are given to show that certain intersections of subsets are nonempty, and conjectures are formulated regarding other intersections of subsets. For example, it is conjectured that all span- $n$ sequences with the two-level autocorrelation property are in class $PN$ . Some relationships between run properties and correlation properties of binary sequences are also obtained.