The linear complexity of related prime sequences
D. H. Green, L. P. Garcia–Perera · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2004
Polyphase related–prime (RP) sequences can be constructed from the modified combination of two polyphase power–residue sequences and are generalizations of the two–phase modified Jacobi sequences, which include the twin–prime sequences as a special case. These sequences have also been referred to as cyclotomic sequences. RP sequences have been conjectured to possess high linear complexity under certain conditions and this is now confirmed theoretically for the q–phase case when q is a prime. The linear complexity of an RP sequence of length Λ= r . s, where r and s are distinct primes, is shown to depend on the relationship between the two primes used in the construction of the sequence and their selected primitive roots, and on the value assigned to the initial digit of the sequence.