To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented,here N is a factor of 2^n-1,where n is an integer.The case is more complicated when the period is even.In this paper,we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k-error linear complexity algorithm.Then,an algorithm for spectral immunity of binary sequence with period N=2^n is obtained.Furthermore,the time complexity of this algorithm is proved to be O（n）.
Quantum pseudo-telepathy(QPT)is a new type of game where the quantum team can win with certainty while the classical one cannot.It means the advantages of quantum participants over classical ones in game.However,there has been no systematic and formal analysis on the QPT game before.Here we present the formal description of the QPT game and the definition of the most simplified QPT.Based on the above definitions,we simplify a famous QPT game,i.e.the Cabllo game.Then,according to some instances,we analyze the minimum best success probability by classical strategies of the two-player QPT,which reflects the advantage of the quantum strategies.Finally,we prove the best success probability by classical strategies for the most simplified QPT is totally related to the number of all possible question combinations.
