Two Families Of Cyclotomic Sequences Based On The Cyclotomic Theory

Because the pseudorandom sequence have balance,long period,low correlation, large linear complexity and other desired properties,the pseudorandom sequence have wide applications in code division multiple access(CDMA)communication system, stream cipher system,radar,coding,etc.The pseudorandom sequence constructed by the cyclotomic theory in the finite fields,we call it cyclotomic sequences.Since the cyclotomic sequence can be easy tO analysis the random properties,it’s meanmgful to construct the pseudorandom sequence with good random properties.In recent years,many scholars have constructed the cyclotomic sequences with low autocorrelation and large linear complexit y.In this paper,for a prime N,N≡ 1(mod 3),we construct a new family of binary cyclotomic sequence of order 3 witll period N.We prove that the new sequence have three autocorrelation and the linear complexity is N-1 when N satisnes thecondition N=a2+12.Secondly,for an odd prime N,N≡1(mod r),where r is a positive integer,a class of almost r—phase sequences with ideal autocorrelation are constructed based on the cyclotomic theory.By modifying the zero element,we get the γ-phase sequences, then disCusses its value distribution,Merit Factor and linear complexity.When r≥3, the Merit Factor of these sequencs is N2/3(N-1)and the linear complexity can be N-1. Moreover,these sequences include some known sequences.