Z4-valued quadratic forms and quaternary sequence families

Z4-valued quadratic forms defined on a vector space over GF(2) are studied. A classification of such forms is established, distinguishing Z4-valued quadratic forms only by their rank and whether the associated bilinear form is alternating or not. This result is used to compute the distribution of certain exponential sums, which occur frequently in the analysis of quaternary codes and quaternary sequence sets. The concept is applied as follows. When t = 0 or m is odd, the correlation distribution of Family S(t), consisting of quaternary sequences of length 2m− 1, is established. Then, motivated by practical considerations, a subset S∗(t) of Family S(t) is defined, and the correlation distribution of Family S∗(t) is given for odd and even m.