On the linear complexity over Fp of quaternary sequences from binary Sidel'nikov sequences

Recently, a quaternary sequence with optimal autocorrelation property is proposed by applying inverse Gray mapping to a pair of binary Sidel'nikov sequences. This quaternary sequence has even period and the maximum nontrivial autocorrelation magnitude is R
_max
= 2, which is optimal and is the first quaternary sequences having R
_max
= 2 for N ≡ 0 mod 4. In this paper, we present a closed-form representation of the linear complexity of the quaternary sequences over F
_p
for p ≥ 5.