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We determine the exact values of the linear complexity of 2p-periodicquaternary sequences over Z_4 (the residue class ring modulo 4) defined fromthe generalized cyclotomic classes modulo 2p in terms of the theory of ofGalois rings of characteristic 4, where p is an odd prime. Compared to the caseof quaternary sequences over the finite field of order 4, it is more dificultand complicated to consider the roots of polynomials in Z_4[X] due to the zerodivisors in Z_4 and hence brings some interesting twists. We answer an openproblem proposed by Kim, Hong and Song.

Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p