Linear Complexity over F p of Ternary Sidel’nikov Sequences

Abstract

AbstractIn this paper, for positive integers m, M, and a prime p such that M|p m – 1, we derive linear complexity over the prime field F p of M-ary Sidel’nikov sequences of period p m – 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 k 0 ≠1 at the (p m –1)/2-th position is nearly close to the period of the sequence, while that with k 0 =1 shows much lower value.KeywordsDiscrete Fourier TransformBinary SequenceLinear ComplexityPrimitive ElementError Control CodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.