Binary Sequences with Autocorrelations and Cross Correlations in a Prescribed Range

摘要

Sequences are surveyed with the property that when a sequence of length n is compared to the same sequence cyclically shifted any number of steps, except for a multiple of the length n, the number of positions where they differ is always (n+1)/2. A method for constructing sets of binary sequences with the property that the autocorrelations and the cross correlations of all sequences within a set fall within a prescribed range is devised. The lengths of the sequences are restricted to 500 to 1200 binary digits. Test cases are presented and comparisons are made with sets of sequences that were chosen at random, showing good results.