Model Families of Quadratic Forms

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.

-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...

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...

Representation of Quadratic Forms by Integral Quadratic Forms

Dynamics of Quadratic Families

This paper is based on the readings in the author’s independent study on ”advanced dynamical systems”, and the author’s mathematics honors project. It is a combination of the survey of some classical papers and the results from the research project. In the review part, none of the results are new and even less of them are due to the author; in the research part, we mainly focus the dynamics of ...