On list-decoding schemes for punctured Reed-Solomon, Gabidulin and subspace codes

Punctured Reed-Solomon (RS) and Gabidulin (G) codes over the field F_qm with locators from the subfield F_q can be represented as interleaving of m correspondent codes over the subfield F_q or can be considered as virtual interleaving of m correspondent codes over the field F_qm. Using an interpolation-based list decoder, m-interleaved or virtually interleaved codes can be decoded up to the same radius mm+T (d - 1), where d is the code distance in the corresponding metric. An explicit root-finding system for the virtual interleaved decoder that can be solved efficiently over F_q is presented. We show that correspondent decoders over the subfield F_q and the field F_qm are equivalent and conclude that in practice one should use a decoder over the subfield since it has less complexity. For m-interleaved codes over F_q a decoding parameters is introduced that allows to control the decoding radius vs. list size trade off.