On minimal polynomials over Fqm and over Fq of a finite-length sequence over F qm

Authors:
Li-Ping Wang
Affiliations:
Institute for Advanced Study, Tsinghua University, Beijing 100084, Peoples Republic of China
Venue:
Finite Fields and Their Applications
Year:
2011

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Abstract

In this paper we consider two problems, finding minimal polynomials over F"q"^"m and over F"q of a finite-length sequence over F"q"^"m, in a lattice and its sublattice respectively using lattice theory over polynomial rings. And we deduce a relationship between them by a lattice basis transformation matrix. As a byproduct, we present a new synthesis algorithm for the first problem just using operations in F"q instead of F"q"^"m as in Berlekamp-Massey algorithm.