Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation

2006 ◽  
Vol 55 (9) ◽  
pp. 1167-1177 ◽  
Author(s):  
J.-C. Bajard ◽  
L. Imbert ◽  
C. Negre
Keyword(s):  
Finite Fields ◽  
Prime Characteristic ◽  
Arithmetic Operations

scholarly journals Commutative rings with homomorphic power functions

1992 ◽  
Vol 15 (1) ◽  
pp. 91-102
Author(s):  
David E. Dobbs ◽  
John O. Kiltinen ◽  
Bobby J. Orndorff
Keyword(s):  
Commutative Ring ◽  
Finite Fields ◽  
Structure Theorem ◽  
Commutative Rings ◽  
Prime Characteristic ◽  
Power Functions ◽  
Finite Case

A (commutative) ringR(with identity) is calledm-linear (for an integerm≥2) if(a+b)m=am+bmfor allaandbinR. Them-linear reduced rings are characterized, with special attention to the finite case. A structure theorem reduces the study ofm-linearity to the case of prime characteristic, for which the following result establishes an analogy with finite fields. For each primepand integerm≥2which is not a power ofp, there exists an integers≥msuch that, for each ringRof characteristicp,Rism-linear if and only ifrm=rpsfor eachrinR. Additional results and examples are given.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Conscious and Unconscious Reward Cues Can Affect a Critical Component of Executive Control

2011 ◽  
Vol 58 (5) ◽  
pp. 370-375 ◽  
Author(s):  
Rémi L. Capa ◽  
Gaëlle M. Bustin ◽  
Axel Cleeremans ◽  
Michel Hansenne
Keyword(s):  
Correct Response ◽  
Executive Control ◽  
Critical Component ◽  
Arithmetic Operations ◽  
Component Process

The present study investigates whether updating an important function of executive control can be driven by unconscious reward cues. Participants had to memorize several numbers and update those numbers independently according to a sequence of arithmetic operations. At the beginning of each trial, a reward (1 euro or 5 cents) was presented, either subliminally or supraliminally. Participants could earn the reward if they found the correct response on the updating task. Results showed better performance when a high (conscious or unconscious) reward was at stake compared to a low reward. This suggests that subliminal information can influence a component process of executive control traditionally thought to require consciousness.

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable
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