scholarly journals On finite field arithmetic in characteristic 2

2020 ◽  
Vol 68 ◽  
pp. 101739
Author(s):  
Tony Ezome ◽  
Mohamadou Sall
Keyword(s):  
Finite Field ◽  
Finite Field Arithmetic ◽  
Characteristic 2

Maximal T-spaces of free associative algebras over a finite field

2018 ◽  
Vol 17 (04) ◽  
pp. 1850064
Author(s):  
C. Bekh-Ochir ◽  
S. A. Rankin
Keyword(s):  
Finite Field ◽  
Positive Characteristic ◽  
Associative Algebras ◽  
Prime Field ◽  
Characteristic 2 ◽  
Infinite Set

In earlier work, it was established that for any finite field [Formula: see text] and any nonempty set [Formula: see text], the free associative (nonunitary) [Formula: see text]-algebra on [Formula: see text], denoted by [Formula: see text], had infinitely many maximal [Formula: see text]-spaces, but exactly two maximal [Formula: see text]-ideals (each of which was shown to be a maximal [Formula: see text]-space). This raises the interesting question as to whether or not the maximal [Formula: see text]-spaces can be classified. However, aside from the two maximal [Formula: see text]-ideals, no examples of maximal [Formula: see text]-spaces of [Formula: see text] have been identified to this point. This paper presents, for each finite field [Formula: see text], an infinite set of proper [Formula: see text]-spaces [Formula: see text] of [Formula: see text], none of which is a [Formula: see text]-ideal. It is proven that for any distinct integers [Formula: see text], [Formula: see text]. Furthermore, it is proven that for the prime field [Formula: see text], [Formula: see text] any prime, [Formula: see text] is a maximal [Formula: see text]-space of [Formula: see text]. We conjecture that for any finite field [Formula: see text] of positive characteristic different from 2 and each integer [Formula: see text], [Formula: see text] is a maximal [Formula: see text]-space of [Formula: see text]. In characteristic 2, the situation is slightly different and we provide different candidates for maximal [Formula: see text]-spaces.

Efficient semisystolic architectures for finite-field arithmetic

1998 ◽  
Vol 6 (1) ◽  
pp. 101-113 ◽  
Author(s):  
S.K. Jain ◽  
L. Song ◽  
K.K. Parhi
Keyword(s):  
Finite Field ◽  
Finite Field Arithmetic
Sign in / Sign up

Export Citation Format

Share Document