Factoring of \(x^ n -1\) and orthogonalization over finite fields of characteristic 2 (Q1340509)

The author presents a new deterministic algorithm which gives a complete factorization of \(x^ n -1\) over a finite field \(F\) of characteristic 2. The main ideas are previously known ones adapted to treating \(F\) as a tower of extensions rather than as a simple extension. For example, the main overall idea is that the problem of factorization may be reduced to computing the set of primitive idempotents of the algebra \(F[ x]/ (x^ n-1)\).