Extension of Rank Test for Sequences over GF(q)

Pseudo-random and random sequences are widely used in many applications, such as stream cipher systems. Statistical tests are usually used to evaluate randomness of sequences. Binary matrix rank test is one method to evaluate randomness of sequences. This test is based on constructing matrices whose rows are successive sub-strings of the sequence, and check for linear dependency among the rows or columns of the constructed matrices. In this paper, we represent new method to testing for randomness based on linear dependency among fixed-length substrings of sequences over GF(q)