TABLE OF CONTENTS A Gold sequence is constructed from a maximal sequence with characteristic polynomial 1 + x 2 + x 3. The second sequence is obtained by decimation of the maximal sequence by q = 3. (a) Find one period of each of the two sequences. Is the second sequence maximal? (b) List the 7 cross-correlation values of this pair of sequences. Show that they are a preferred pair.
The characteristic polynomials for generating Gold sequences of length 7 are: f 1(x) = 1 + x + x 3 and f 2(x) = 1 + x 2 + x 3. (a) What is the generating function for the maximal Gold sequence generated by f 1(x) and initial contents 100? (b) What is the generating function for the maximal Gold sequence generated by f 2(x) and initial contents 100? (c) What is the general expression for the generating function of an arbitrary nonmaximal Gold sequence? (d) What is the generating function for the Gold sequence generated by adding the sequences in (a) and (b)? (e) What is the value at k = 0 of the periodic cross correlation between the sequences in (a) and (b)?
A small set of Kasami sequences is formed by starting with the maximal sequence generated by the characteristic polynomial 1 + x 2 + x 3 + x 4 + x 8. After decimation by q,...
