scholarly journals Abelian Groups, Gauss Periods, and Normal Bases

2001 ◽  
Vol 7 (1) ◽  
pp. 149-164 ◽  
Author(s):  
Shuhong Gao
Keyword(s):  
Abelian Groups ◽  
Normal Bases ◽  
Gauss Periods

scholarly journals MULTIPLICATIVE ORDER OF GAUSS PERIODS

2010 ◽  
Vol 06 (04) ◽  
pp. 877-882 ◽  
Author(s):  
OMRAN AHMADI ◽  
IGOR E. SHPARLINSKI ◽  
JOSÉ FELIPE VOLOCH
Keyword(s):  
Lower Bound ◽  
Finite Fields ◽  
Normal Bases ◽  
Multiplicative Order ◽  
Gauss Periods

We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.

Gauss periods as constructions of low complexity normal bases

2011 ◽  
Vol 62 (1) ◽  
pp. 43-62 ◽  
Author(s):  
M. Christopoulou ◽  
T. Garefalakis ◽  
D. Panario ◽  
D. Thomson
Keyword(s):  
Low Complexity ◽  
Normal Bases ◽  
Gauss Periods

scholarly journals Normal bases via general Gauss periods

1999 ◽  
Vol 68 (225) ◽  
pp. 271-291 ◽  
Author(s):  
Sandra Feisel ◽  
Joachim von zur Gathen ◽  
M. Amin Shokrollahi
Keyword(s):  
Normal Bases ◽  
Gauss Periods

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

Sign in / Sign up

Export Citation Format

Share Document