An Alternative Method for Primary Decomposition of Zero-dimensional Ideals over Finite Fields

摘要

We present an alternative method for computing primary decomposition ofzero-dimensional ideals over finite fields. Based upon the furtherdecomposition of the invariant subspace of the Frobenius map acting on thequotient algebra in the algorithm given by S. Gao, D. Wan and M. Wang in 2008,we get an alternative approach to compute all the primary components at once.As one example of our method, an improvement of Berlekamp's algorithm bytheoretical considerations which computes the factorization of univariatepolynomials over finite fields is also obtained.