The relations of Barratt and Miller are shown to include all relations among the elements in the mod Steenrod algebra, and a minimal set of relations is given.
"More on the anti-automorphism of the Steenrod algebra." Algebr. Geom. Topol. 11 (5) 2579 - 2585, 2011. https://doi.org/10.2140/agt.2011.11.2579