On the computation of ExtAk,k+*(Z/2,Z/2) for k ≤ 5

This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, ExtAk, k+*(Z/2, Z/2) for k ≤ 5, based on the well-known generators and the Adams relations given in Chen's work [2]. The purpose of this algorithm is to verify the hand-computed results for ExtA4, 4+*(Z/2, Z/2) presented in our corrected papers [8, 9, 10]. Combining our most recent works [11, 12], the verification of the domain and the codomain of the fourth algebraic transfer in specific degrees can now be completed.