A matrix membership test recasts the hit problem as linear algebra, and a SageMath implementation yields dim(QP5)_64 = 1690 (not 1694) and dim(QP5)_128 = 1985.
Hung, The cohomology of the Steenrod algebra and representations of the general linear groups , Trans
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A matrix criterion and algorithmic approach for the Peterson hit problem: Part I
A matrix membership test recasts the hit problem as linear algebra, and a SageMath implementation yields dim(QP5)_64 = 1690 (not 1694) and dim(QP5)_128 = 1985.