We show that when gcd(n,w) = 1, the set of binary words of length n and weight w can be partitioned to give n maximal w-weight codes. It follows that under the same hypothesis, the least cardinal of a maximal constant weight code is at most 1/n times n choose w.
Prem L Sharma
"An Array of Disjoint Maximal Constant Weight Codes,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 5:
1, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol5/iss1/1