 noted that for n in the vicinity of a run of L - 1 zeros in an m-sequence, Paa(K, n, T) had lower correlation values, as T varied around zero, for m-sequences whose characteristic polynomials contained more non-zero coefficients. Wainberg and Wolf [17] compared the moments of K-tuple weight distrib- utions for m-sequences over GF(2) to the corresponding moments for a purely random sequence, and, extending Lindholm's work, carried this out through the sixth moment with K VI 100 for several sequences. Fredriccson [18] carried this idea closer to the realm of coding theory by noting that the set of N-tuples consisting of one period of an m-sequence and all its cyclic shifts, and the all-zeros N-tuple, together form a linear code which is the dual of a single-error-correcting Hamming code. Since the set n , bn+k-1) n=1,2, N} of K-tuples along with the all-zeros K-tuple form a punctured version of this m-sequence code, the set's dual is a short- ened Hamming code. The weight distribution of the shortened Hamming code can be related in turn to the moments of the weight distribution of K- tuples from {bn} by the MacWilliams-Pless identities [19]. Bekir [20] extended this approach by applying moment techniques [21], [22] to generate upper and lower bounds on the distribution function of partial-period correlation values. 5.5 GALOIS FIELD CONNECTIONS 5.5.1 Extension Field Construction The reader with no prior knowledge of finite field structures is urged at this point to review Appendix 5A, for the connection between certain LFSRs and finite fields will now be clarified. Assume that one has mechanized arithmetic units to carry out addition and multiplication in a finite field GF(q) which we will refer to as the ground field. In many practical designs the ground field is GF(2) since modulo 2 arithmetic units are available. Let ma(z) be an irreducible polynomial of degree d over GF(q), d > 1, with a root called a; ma(z) is termed the minimum polynomial of a over GF(q). Certainly, a is not a member of GF(q), or else ma(z) w