Abstract:

Pseudorandom sequences play an important role in information security system. Although there are many sequences have been given and studied, the search for new approaches and new constructions should be continued. The construction methods and pseudorandom analysis is the main research content of pseudorandom theory. The well-distribution measure, correlation measure, collision and avalanche effect become the important indexes of pseudorandom sequences to determine good or bad. In a series of papers Mauduit and others introduced and studied the measures of finite sequences of k symbols. In this paper we construct a large family of pseudorandom sequences of k symbols with length pq by using Ding-Helleseth generalized cyclotomic classes, and study the well-distribution measure, correlation measure, collision and avalanche effect by using the properties of trigonometric identity, exponential sum and character sum.

Key words: pseudorandom sequences of k symbols, cyclotomic class, character sum