I know the definition of a field but I haven't really studied much algebra. Can someone tell me what this means:
I know it involves a 2-element field but that's about it.
it's a quotient ring. the "main ring" is the ring of polynomials in x and y, with coefficients in the 2-element field F2 = {0,1}. that ring is being factored via the ideal generated by two polynomials x^r and y^s (that is, any polynomial of the form p(x,y)x^r + q(x,y)y^s is treated as if it was 0, so basically this knocks off all powers of x higher than r-1, and all powers of y higher than s-1).