Higher-order OSD improves by testing non-zero configurations for the remainder bits $bold(e)_([T])$.
For any chosen hypothesis $bold(e)([T])$, the corresponding basis bits $bold(e)([S])$ are uniquely determined to satisfy the syndrome:
$ bold(e)([S]) = H([S])^(-1) dot (bold(s) + H_([T]) dot bold(e)_([T])) $
By introducing a better serch method in the uncertain vector space?