Ludovicus Marinus Gerardus Maria Tolhuizen

Efficient encoding for a class of subspace subcodes

Let S consist of all words of a code C for which each symbol is in a stipulated subalphabet, possibly different for distinct positions. We consider the special case where C is a linear maximum-distance separable (MDS) code, and the subalphabets are linear subspaces over the ground field with equal dimensions. We give an explicit algorithm for selecting the subspaces in such a way that a straightforward systematic encoding algorithm, based on an encoder for C, can be applied. The number of information symbols that can be encoded with this algorithm equals a well-known lower bound on the dimension of S.