On the bounds of the bilinear complexity of multiplication in some finite fields

DOI10.1007/s00200-004-0155-7zbMath1086.11027OpenAlexW2085888905MaRDI QIDQ1762551

Stéphane Ballet, Jean Chaumine

Publication date: 9 February 2005

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-004-0155-7

zbMATH Keywords

finite fieldsalgebraic curvesalgebraic function fieldsBilinear complexity

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Arithmetic theory of algebraic function fields (11R58) Arithmetic ground fields for curves (14H25) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)

Related Items (8)

An improvement of the construction of the D. V. and G. V. Chudnovsky algorithm for multiplication in finite fields ⋮ On some bounds for symmetric tensor rank of multiplication in finite fields ⋮ On the tensor rank of multiplication in any extension of \(\mathbb F_2\) ⋮ On the tensor rank of the multiplication in the finite fields ⋮ On multiplication in finite fields ⋮ On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields ⋮ On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry ⋮ New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields

Cites Work

• Unnamed Item
• Algebraic function fields and codes
• On the existence of non-special divisors of degree \(g\) and \(g-1\) in algebraic function fields over \(\mathbb{F}_2\)
• On multiplication in algebraic extension fields
• A new construction of algebraic-geometry codes
• Low increasing tower of algebraic function fields and bilinear complexity of multiplication in any extension of \(\mathbb F_q\)
• Multiplication algorithm in a finite field and tensor rank of the multiplication.
• Curves with many points and multiplication complexity in any extension of \(\mathbb{F}_q\)
• Characterization of Division Algebras of Minimal Rank and the Structure of their Algorithm Varieties
• Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves
• On tame towers over finite fields

This page was built for publication: On the bounds of the bilinear complexity of multiplication in some finite fields