The linear complexity of whiteman's generalized cyclotomic sequences of period p {m+1}q n+1

摘要

In this paper, we mainly get three results. First, let p, q be distinct primes with gcd ((p-1)p,(q-1)q)=gcd (p-1,q-1)=e ; we give a method to compute the linear complexity of Whiteman's generalized cyclotomic sequences of period p^{m+1}q n+1. Second, if e=4, we compute the exact linear complexity of Whiteman's generalized cyclotomic sequences. Third, if p equiv q equiv 5∼({m mod}∼8), gcd (p-1, q-1)=4, and we fix a common primitive root g of both p and q, then 2in H-{0}=(g), which is a subgroup of the multiplicative group Z-{pq} st, if and only if Whiteman's generalized cyclotomic numbers of order 4 depend on the decomposition pq=a^{2}+4b 2 with 4ert b. © 1963-2012 IEEE.