A Class of Quadratic Matrix Equations over Finite Fields
نویسندگان
چکیده
We exhibit an explicit formula for the cardinality of solutions to a class quadratic matrix equations over finite fields. prove that orbits these under natural conjugation action general linear groups can be separated by classical invariants defined characteristic polynomials. also find generating set vanishing ideal orbits.
منابع مشابه
Pairs of Quadratic Forms over Finite Fields
Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...
متن کاملPencils of quadratic forms over finite fields
A formula for the number of common zeros of a non-degenerate pencil of quadratic forms is given. This is applied to pencils which count binary strings with an even number of 1’s prescribed distances apart.
متن کاملA Class of Polynomials over Finite Fields
Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points. 1999 Academic Press
متن کاملExponents of Class Groups of Quadratic Function Fields over Finite Fields
We find a lower bound on the number of imaginary quadratic extensions of the function field Fq(T ) whose class groups have an element of a fixed order. More precisely, let q ≥ 5 be a power of an odd prime and let g be a fixed positive integer ≥ 3. There are q 1 2+ 1 g ) polynomials D ∈ Fq[T ] with deg(D) ≤ ` such that the class groups of the quadratic extensions Fq(T, √ D) have an element of or...
متن کاملExtremal Trinomials over Quadratic Finite Fields
In the process of pursuing a finite field analogue of Descartes’ Rule, Bi, Cheng, and Rojas (2014) proved an upper bound of 2 √ q − 1 on the number of roots of a trinomial c1 + c2x a2 + c3x a3 ∈ Fq [x], conditional on the exponents satisfying δ = gcd(a2, a3, q − 1) = 1, and Cheng, Gao, Rojas, and Wan (2015) showed that this bound is near-optimal for many cases. Our project set out to refine the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2022
ISSN: ['0219-1733', '1005-3867']
DOI: https://doi.org/10.1142/s1005386723000147