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

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