Let F be a finite field of cliaracteristic two and'let F'xm and FIXn denote vector spaces of m-tuples and n-tuples, respectively, over P. Let Q be a quadratic form of rank m defined on FIXm and let Q, be a quadratic form of rank n defined on F I X n . Then relative to given ordered bases for .FIXm a
Representations of Forms by Forms in a Finite Field
β Scribed by Z.-X. Wan
- Book ID
- 102966582
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 672 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1071-5797
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β¦ Synopsis
Let (F_{c}) be a finite field with (q) elements, where (q) is a prime power which may be either odd or even. Representations of a form by another form of the same type in (\sqrt{F}_{4}) are studied and formulas of the number of representations are obtained. Forms considered in this paper include bilinear forms, alternate bilinear forms, hermitian forms, quadratic forms, and symmetric bilinear forms. 1995 Academic Press. Inc.
π SIMILAR VOLUMES
Using the CREP system we show that matrix representations of representation-finite algebras can be transformed into normal forms consisting of (0, 1)-matrices.
In this article, we provide the complete answer to a question raised by Kitaoka in his book. (1999, ``Arithmetic of Quadratic Forms,'' Cambridge Univ. Press, Cambridge, UK). More precisely, we prove that A 4 = ( 4) represents all but one and D 4 20[2 1 2 ] represents all but three binary positive ev