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On Mutually Orthogonal Extraordinary Supersquares
Let F d be the finite field with d elements. Extraordinary subgroups in F d × F d play an important role in the field of quantum information theory,...
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Chebyshev Polynomials and Pell Equations over Finite Fields
We shall describe how to construct a fundamental solution for the Pell equation x 2 − my 2 = 1 over finite fields of characteristic p ≠ 2. Especially,...
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Construction of the mutually orthogonal extraordinary supersquares
Our purpose is to determine the complete set of mutually orthogonal squares of order d , which are not necessary Latin. In this article, we introduce...
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Regular orbits on the deleted permutation module
Let S d denote the symmetric group of degree d . Let F be the field of r elements, and let S ( d , r ) = S d × F *. Let V ( d , r ) be the deleted permutation...
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An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field
In this paper we give a term equivalence between the simple k -cyclic Post algebra of order p, L p,k , and the finite field F ( p k ) with constants F ( p )....
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A Review on the Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Finite Fields Admitting a Weierstrass Point
The reduced equations for the isomorphism classes of hyperelliptic curves of genus 2 admitting a Weierstrass point over a finite field of arbitrary...
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Normal Bases and Their Dual–Bases over Finite Fields
In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the...
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The Number of Nonisomorphic Two-dimensional Algebras over a Finite Field
In this paper, we derive explicit formulas for the number of nonisomorphic two-dimensional nonassociative algebras, possibly without a unit, over a...
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The Primitive Idempotents of a Cyclic Group Algebra
Explicit expressions are obtained for the 2 n + 1 primitive idempotents in FG , the semisimple group algebra of the cyclic group G of order p n ( p an...
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Linear and quadratic sections of Grassmannians over a finite field
Here we study the Finite Field Nullstellensatz for linear and quadratic sections of the Grassmannians of lines.
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Division Algebras, Galois Fields, Quadratic Residues
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more...
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Program correctness on finite fields
An asserted program is presented whose correctness is provable by the Floyd-Hoare-Naur method in each finite field separately, which, however, admits...
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