Trace- and norm-compatible extensions of finite fields (Q1205131)

The author defines the notion of trace-compatibility in analogy to the notion of norm-compatibility for extensions of a field. Extensions that are norm-compatible or trace-compatible are computationally easier to handle. An algorithm for the computation of trace-compatible polynomials is given. The number of distinct (norm- or trace-) compatible polynomials of fixed degree is counted. There are two misprints: p. 200 4th line from the bottom: \(F_{q^ m}\) must be \(F_{q^ m}^*\), p. 201 line 21: log must be Log. The paper is written in a very compact way and therefore it has become more or less opaque. The results, however, are nice.