A new family of Fq-linear codes over Fbq can be obtained replacing the elements in the large field Fqb by elements in Fq[C], where C is the companion matrix of a primitive polynomial of degree b and coefficients in Fq. In this work, we propose a decoding algorithm for this family of Fq-linear codes over the erasure channel, based on solving linear systems over the field Fq.The work of the first author was partially supported by a grant for postdoctoral students from FAPESP with reference 2015/07246-0
