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Recently a construction of optimal non-constant dimension subspace codes,also termed projective space codes, has been reported in a paper ofHonold-Kiermaier-Kurz. Restricted to binary codes in a 5-dimensional ambientspace with minimum subspace distance 3, these optimal codes were interpreted interms of maximal partial spreads of 2-dimensional subspaces. In a paralleldevelopment, an optimal binary (5,3) code was obtained by a minimal changestrategy on a nearly optimal example of Etzion and Vardy. In this article, wereport several examples of optimal binary (5,3) codes obtained by theapplication of this strategy combined with changes to the spread structure ofexisting codes. We also establish that, based on the types of constituentspreads, our examples lie outside the framework of the existing construction.

Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads