Complementary vertical bipolar transistor process using high-energy ion implantation

Abstract

ReferencesTaking into account that j = x"I2 and x" = -1 in evaluating eqns. 6 and 9, the coefficients ci of C(x) can be obtained from the complex coefficients of eqns. 9 and 10 as follows:Example: Consider two eight-point sequences A = (ao, . . . , a,) = (5, 2, 6, 9, 3, 4, I, 10) and B = ( b o , . . . , b , ) = (4, 10, 2,8,5,7,6,3) and consider the computation of their skew cyclic convolution C = (e,,, . . . , c7) with arithmetic performed modulo 17. The traditional way of computing it (based on eqn. 6), requires 8' = 64 multiplications and the result is C = (e,,, ..., c7) = (-234, -83, -104, 50, 67, 94, 166, 196), and by evaluating each ci modulo 17 we obtain C = (c,,, . . . , c7) = (4, 2, 15, 16, 16,9, 13.9). On the other hand, the same task can be computed using the QRNS with only 32 multiplications in the QRNS domain. Because 17 is prime and 17 = 4 x 4 + 1, then according to theorem 1, x2 f 1 = 0 is solvable in Z,, and the QRNS mapping exists, and j = 4 is one root of x2 + 1 = 0 in