Explicit formulas for self-complementary normal bases in certain finite fields

1991 ◽  
Vol 37 (4) ◽  
pp. 1220-1222 ◽  
Author(s):  
A. Lempel ◽  
G. Seroussi
Keyword(s):  
Finite Fields ◽  
Explicit Formulas ◽  
Normal Bases

scholarly journals Optimal Normal Bases Over Finite Fields

2021 ◽  
Vol 67 (6) ◽  
pp. 58-61
Author(s):  
Duggirala Meher Krishna ◽  
Duggirala Ravi
Keyword(s):  
Finite Fields ◽  
Normal Bases

scholarly journals Constructing normal bases in finite fields

1990 ◽  
Vol 10 (6) ◽  
pp. 547-570 ◽  
Author(s):  
Joachim von zur Gathen ◽  
Mark Giesbrecht
Keyword(s):  
Finite Fields ◽  
Normal Bases

QUADRATIC FORMULAS FOR GENERALIZED QUATERNIONS

2009 ◽  
Vol 08 (03) ◽  
pp. 289-306 ◽  
Author(s):  
MARCO ABRATE
Keyword(s):  
Finite Fields ◽  
Quaternion Algebra ◽  
Quadratic Polynomial ◽  
Explicit Formulas ◽  
Quaternion Algebras ◽  
Solving Equations ◽  
Generalized Quaternion

In this paper we derive explicit formulas for computing the roots of a quadratic polynomial with coefficients in a generalized quaternion algebra over any field 𝔽 with characteristic not 2. We also give some example of applications for the derived formulas, solving equations in the algebra of Hamilton's quaternions ℍ, in the ring M2(ℝ) of 2 × 2 square matrices over ℝ and in quaternion algebras over finite fields.

Construction of Normal Bases over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 1-11
Author(s):  
PROF. P. L. SHARMA ◽  
◽  
Kiran Devi ◽  
Arun Kumar ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Normal Bases
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