Using a computer-aided approach, we classify inequivalent binary extended $1$-perfect bitrades of length $10$, constant-weight extended $1$-perfect bitrades of length $12$, and STS bitrades derived from them. As a corollary, we see that there is only one pair of disjoint Steiner sextuple systems S$(5,6,12)$, up to equivalence. Keywords: bitrades, $1$-perfect code, Steiner trades, small Witt design.
['Denis S. Krotov']
The extended 1-perfect trades in small hypercubes