Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of \(\ell\)-Interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity \(O(\ell \mu^2)\) where \(\mu\) measures the size of the input problem.