PATTERN DISTRIBUTIONS OF LEGENDRE SEQUENCES

Legendre sequences have a number of interesting randomness properties and are closely related with quadratic residue codes. In this correspo ndence we give lower and upper bounds on the number of patterns distri buted in a cycle of the Legendre sequences and establish the relations hip between the weight distribution of quadratic residue codes and the pattern distribution of Legendre sequences. Our result shows that Leg endre sequences have an ideal distribution of patterns of length s, wh en s is not large compared with log(2) N, where N is the prime used to define the sequence.