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Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p
We determine the exact values of the linear complexity of 2p-periodic
quaternary sequences over Z_4 (the residue class ring modulo 4) defined from
the generalized cyclotomic classes modulo 2p in terms of the theory of of
Galois rings of characteristic 4, where p is an odd prime. Compared to the case
of quaternary sequences over the finite field of order 4, it is more dificult
and complicated to consider the roots of polynomials in Z_4[X] due to the zero
divisors in Z_4 and hence brings some interesting twists. We answer an open
problem proposed by Kim, Hong and Song