On the Quadratic Spans of Periodic Sequences

Abstract

Random binaxy sequences are required in many applications of modern communi- cation systems and in designing reliable circuits. However, truly random sequences are often associated with extremely high costs, and are therefore infeasible to use. Deter- ministically generated sequences that pass certain statistical tests suggested by random sequences are often used instead and are referred to as pseudorandom sequences. In applications involving, for instance, secure or spread spectrum communications, it is essential that these pseudorandom sequences be unpredictable. This paper addresses the problem of predicting the terms of a pseudorandom sequence from some initial por- tion of the sequence. A good introduction to the issues involved in this area can be found in [7].