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

Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation