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. Paper 52.