580 California St., Suite 400
San Francisco, CA, 94104
Figure 1 – uploaded by Mark Manasse
Figure 1 When we take an arbitrary m by m submatrix of this coding matrix, evaluating the determinant by picking available columns from the identity portion of the matrix makes it clear that the determinant is equal (up to sign, which is irrelevant over a field of characteristic two) to the determinant of the 0 by 0, | by 1, 2 by 2, or For our use, let g be a generator of the finite field. The elements from which we generate our Vandermonde matrix are g° (i.e., 1), g! (i.e., g), and g*. More explic- itly, if our coding matrix is M, for i < m, and j < m, Mjj = 5, and Mi (n+e = git for k = 0, 1, or 2. More explicitly, M can defined as follows: