  We first find the combinatorial degree of any map $f:V\to F$ where $F$ is a
finite field and $V$ is a finite-dimensional vector space over $F$. We then
simplify and generalize a certain construction due to Chein and Goodaire that
was used in characterizing code loops as finite Moufang loops that posses at
most two squares. The construction yields binary codes of high divisibility
level with prescribed Hamming weights of intersections of codewords.
