Pseudorandom sequences are one of commonly used test signals in system identification (Ljung, 1999; Soderstrom and Stoica, 1989). In this report, we first extend the concept of binary pseudorandom sequences to GF (q=p^m) valued pseudorandom sequences, define maximal length sequences, characterize their generator polynomials, and describe a computationally fast randomized technique for generating such polynomials. The main problem studied in this report is the construction of a time invariant mapping from MPRS (GF(p^m),n) onto MPRS (GF(p),mn). It is also shown that this is an m to 1 surjection, and its effect is characterized in frequency domain as well. The problems studied in this report are of more technical nature, and motivated by the problems discussed in Toker and Emara-Shabaik, 2002.