Bounds on Single-Exclusion Numbers and Stopping Redundancy of MDS Codes

New bounds on single-exclusion numbers are obtained via probabilistic arguments, recurrent relations, as well as explicit constructions. The new bounds are used to better understand the stopping redundancy of MDS codes. In particular, it is shown that for any fixed k, the stopping redundancy of a linear [n, k] MDS code is between 1/k+1(
_k

ⁿ
) and (1 + o(1))1/k (
_k

ⁿ
).