ers-of-a representation. Since the index n in {bn} usually denotes a discrete time value and since 8 multiplies n in (5.147), we will refer to the elements 8 of the set A in (5.147) as time coefficients. Theorem 5.9 can be rephrased to state that the linear span of {bn} is the number of distinct time coefficients in the powers-of-a repre- sentation of {bn}. Example 5.10. Consider the binary 6-stage LFSR with primitive character- istic polynomial 26 + z superscript(5) + z2 + z + 1, to which has been added NLFFL as shown in Figure 5.10(a). By loading the register with Tr24(a)), i = 0, , 5, i.e., 011111, where a is a root of the LFSR's characteristic polynomial, the sequences in Figure 5.10(b) are produced at different points in the genera- tor. One full period is shown, with the first bit corresponding to index n = 0. The contents of the individual storage elements have been expressed as the trace functions indicated in the above diagram, in accordance with Theorem 5.6. These functions, having domain GF(64) and range GF(2), are defined as (5.163) The NLFFL output sequence {bn} can be represented in terms of the stor- Tr(a"): 011111101011100011001110110000011110010010101001101000010001011 Tr(an+4): 111010111000110011101100000111100100101010011010000100010110111 b,(2): 111101010100000000010100000000110000000101000001000000000010010 (010100100000000000001000000000001000000000100000000000000001001 010011001100110011110000000111011100101111111011000100010101100 Figure 5.10(b). Sequences produced at key locations within the generator of Example 5.10. Non-Linear Feed-Forward Logic age element sequences by bn =Tr(an+4)+Tr(an+1)Tr(an+3) = Tr2(a21n+21). (5.164) Formed by substitution of (5.163) and simplification, the right side of (5.164) contains trace expressions with different domains; hence, domain and range are specified for each term. The above calculation is tedious and, even for this example, is more easily done by computer. By applying Theorem 5.9 and counting the terms in the trace functions of (5.164), namely six