${\BBZ}_4$-Valued Quadratic Forms and Quaternary Sequence Families
Kai-Uwe Schmidt · IEEE Transactions on Information Theory · 2009
In this paper, Zopf4-valued quadratic forms defined on a vector space overGF(2)are studied. A classification of such forms is established, distinguishing Zopf4-valued quadratic forms only by their rank and whether the associated bilinear form is alternating. 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. Whent=0 ormis odd, the correlation distribution of familyS(t), consisting of quaternary sequences of length2m-1, is established. Then, motivated by practical considerations, a subsetS*(t) of familyS(t) is defined, and the correlation distribution of familyS*(t) is given for odd and evenm.