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In this paper, we mainly get three results. First, let p, q be distinct primes with ((p-1)p,(q-1)q)=(p-1,q-1)=e ; we give a method to compute the linear complexity of Whiteman's generalized cyclotomic sequences of period pm+1qn+1. Second, if e=4, we compute the exact linear complexity of Whiteman's generalized cyclotomic sequences. Third, if p≡q 5 (mod 8), gcd(p-1, q-1)=4, and we fix a common primitive root g of both p and q, then 2∈H0=(g), which is a subgroup of the multiplicative group Z*pq, if and only if Whiteman's generalized cyclotomic numbers of order 4 depend on the decomposition pq=a2+4b2 with 4|b.
Date of Publication: Aug. 2012