Complexity of prime-dimensional sequences over a finite field

V.?I. Arnold has recently defined the complexity of a sequence of n zeros and ones with the help of the operator of finite differences. In this paper we describe the results obtained for almost most complex sequences of elements of a finite field, whose dimension n is a prime number. We prove that, with n→∞, this property is inherent in almost all sequences, while the values of multiplicative functions possess this property with any n different from the characteristic of the field. We also describe the prime values of the parameter n which make the logarithmic function almost most complex. All these sequences reveal a stronger complexity; its algebraic sense is quite clear.