Almost regular quaternary quadratic forms

Gonii: Universal Quaternary Quadratic Forms

We continue our study of quadratic forms using Geometry of Numbers methods by considering universal quaternary positive definite integral forms of square discriminant. We give a small multiple theorem for such forms and use it to prove universality for all nine universal diagonal forms. The most interesting case is x2 + 2y2 + 5z2 + 10w2, which required computer calculations.

-Valued Quadratic Forms and Quaternary Sequence Families

In this paper, -valued quadratic forms defined on a vector space over are studied. A classification of such forms is established, distinguishing -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 s...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Five regular or nearly-regular ternary quadratic forms

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...