ector space is 1 and E0, and the coefficients and yo are in GF(2). Then a point in the intersection of ys and S corresponds to a solution of the equation (y180+ (SEO + o) = S'E0 o (5.338) for the unknowns 8 and 8' in GF(2). The element &of can also be represented as e1&0 + eo, where e1 and eo are in GF(2) and eo is not 0. A similar repre- sentation may be used for the element O. This reduces the solution of (5.338) to the solution of a pair of linear equations over GF(2), by setting the coefficients of the basis elements E0 and 1 to zero, giving (y1e1 + yo + 1)00. (5.339) These equations are linearly independent and have a unique solution, except when = 0 and yo = 1, corresponding to the uninteresting case when y = 1. Therefore, (5.334) is satisfied, there being a single point in the intersection ysn's when y & GF(2), and hence, design objective P-2 has been achieved. The choice of o can now be made SO that r2(0) is zero, by requiring that o not be of the form del for any 8 in GF(2), i.e., by requiring that o not be in range (l). The specification of range (l) in (5.335) may be used to determine a suit- able choice for M. Let 1, OK be a basis for GF(2), and let by the vec- tor composed of these basis elements. Then, equating EOD=My (5.340) guarantees by (5.329) that range (l) matches the designed range specified in (5.335). Multiplying the i-th entry of the vector in (5.340) by Bj, taking the trace of the result, and using the fact that y is a vector of elements from a complementary basis for (B:: = 1,...,d} gives the ij-th element of M to be (5.341) Pseudonoise Generators Thus, the elements of M can be determined by trace calculations. The design can be completed by choosing a vector S SO that Tr(ox) = s'x, (5.342) the requirement that o not be in the range (l) corresponding to St not being in the row space of M. It is worth noting that both transforms were useful at certain points in the derivation, but neither transform need be mechanized. Furthermore, com- pletion of a design does not require the determinatio