An Embedding Theorem for Partial Linear Spaces.

Suppose we are given a partial linear space sG (n,m) with n sup 2 + m points and n sup 2 + n+m lin e sub of size n . We prove that it is possible to embed sG (n,m) in a partial linear space sB (n,m) with n sup 2 + n + m+1 points and n sup 2 + n + m+1 lin e sub of size n+1, where every point is on n+1 lines and every line has m parallels. This embedding theorem can be restated in terms of upper bounds on the size A(N,d,w) of the largest binary code with block length N , co n sub tant weight w , and distance d , in the c a sub e N= n sup 2 + m, w= n, and d= 2 (n-1).