Statistical properties of half-l-sequences

摘要

We study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2, which are called half-l-sequences. More precisely, for any N > 1 our first aim is to give upper bounds on the number of occurrences of two symbols with a fixed distance between them and the number of occurrences of three consecutive symbols using certain character sums. Our second aim is to give a bound on the autocorrelation of half-l-sequences for N = 2. Finally, we give bounds on the number of occurrences of two symbols with a fixed distance between them in an l-sequence and obtain conditions on the connection integer that guarantee the distribution is highly uniform.