Identifying high-dimension subspace subcodes of Reed-Solomon codes

Subspace subcodes of Reed-Solomon (SSRS) codes were introduced by Hattori, McEliece, Solomo, and Lin in the mid-1990s. These authors found a complicated dimension formula and a simple, tight lower bound on the dimension of SSRS codes over F₂^m. We prove a conjecture of Hattori concerning how to identify subspaces that can be used to build SSRS codes whose dimension exceeds this lower bound.