Linear Complexity over Fp of Ternary Sidel'nikov Sequences

In this paper, for positive integers m, M , and a prime p such that M |pm − 1, we derive linear complexity over the prime field Fp of M -ary Sidel’nikov sequences of period pm−1 using discrete Fourier transform. As a special case, the linear complexity of the ternary Sidel’nikov sequence is presented. It turns out that the linear complexity of a ternary Sidel’nikov sequence with the symbol k0 = 1 at the (p − 1)/2-th position is nearly close to the period of the sequence, while that with k0 = 1 shows much lower value.