We simplify the proofs of four results in , restating two of them for greater clarity. The main purpose of this note is to give a brief transparent proof of Theorem 7 of , the main upper bound of that paper. The secondary purpose is to give a more direct statement and proof of the integer programming determination of covering radius of . Theorem 7 of  follows from a simple result in , which we state with the notation (for the linear code A).
Mattson, H. F. Jr, "Simplifications to "A New Approach to the Covering Radius...”" (1990). Electrical Engineering and Computer Science - Technical Reports. 52.