Linear complexity of sequences over arbitrary symbols and constructions of sequences over GF(p/sup k/) whose characteristic polynomial is over GF(p)

We propose an appropriate approach of defining the linear complexity of sequences over an unknown symbol set. We are able to characterize those p-ary sequences whose k-tuple versions now over GF(p/sup k/) have the same characteristic polynomial as the original with respect to any basis. This leads to a construction of p/sup k/-ary sequences whose characteristic polynomial is essentially over GF(p).