On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
From MaRDI portal
Publication:4992045
DOI10.1070/RM9928zbMath1482.11164arXiv1906.07456WikidataQ114102357 ScholiaQ114102357MaRDI QIDQ4992045
Stéphane Ballet, Jean Chaumine, Julia Pieltant, Matthieu Rambaud, Robert Rolland, Hugues Randriambololona
Publication date: 4 June 2021
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1906.07456
Analysis of algorithms and problem complexity (68Q25) Number-theoretic algorithms; complexity (11Y16) Finite fields (field-theoretic aspects) (12E20) Algebraic functions and function fields in algebraic geometry (14H05)
Related Items (10)
Optimization of the scalar complexity of Chudnovsky\(^2\) multiplication algorithms in finite fields ⋮ The quadratic hull of a code and the geometric view on multiplication algorithms ⋮ Non-minimum tensor rank Gabidulin codes ⋮ Chudnovsky-type algorithms over the projective line using generalized evaluation maps ⋮ Chaining multiplications in finite fields with Chudnovsky-type algorithms and tensor rank of the \(k\)-multiplication ⋮ Polynomial constructions of Chudnovsky-type algorithms for multiplication in finite fields with linear bilinear complexity ⋮ Finite field arithmetic in large characteristic for classical and post-quantum cryptography ⋮ The equivariant complexity of multiplication in finite field extensions ⋮ Trisymmetric multiplication formulae in finite fields ⋮ Construction of asymmetric Chudnovsky-type algorithms for multiplication in finite fields
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \((2,1)\)-separating systems beyond the probabilistic bound
- Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
- Effective arithmetic in finite fields based on Chudnovsky's multiplication algorithm
- Multiplication of polynomials modulo \(x^n\)
- On the existence of non-special divisors of degree \(g\) and \(g-1\) in algebraic function fields over \(\mathbb{F}_2\)
- An improvement of the construction of the D. V. and G. V. Chudnovsky algorithm for multiplication in finite fields
- On the tensor rank of the multiplication in the finite fields
- On multiplication in finite fields
- Computation of a cover of Shimura curves using a Hurwitz space
- On the complexity of multiplication in finite fields
- An optimal algorithm for multiplication in \(\mathbb{F}_{256}/\mathbb{F}_ 4\)
- On the optimal evaluation of a set of bilinear forms
- On multiplication in algebraic extension fields
- 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.
- Algorithms for exponentiation in finite fields
- Quasi-optimal algorithms for multiplication in the extensions of \(\mathbb F_{16}\) of degree 13, 14 and 15
- Tower of algebraic function fields with maximal Hasse-Witt invariant and tensor rank of multiplication in any extension of \(\mathbb{F}_2\) and \(\mathbb{F}_3\)
- Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields
- Gaps between prime numbers and tensor rank of multiplication in finite fields
- An explicit result for primes between cubes
- On the bounds of the bilinear complexity of multiplication in some finite fields
- Curves with many points and multiplication complexity in any extension of \(\mathbb{F}_q\)
- A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
- Canonical models of arithmetic \((1; e)\)-curves
- On the construction of the asymmetric Chudnovsky multiplication algorithm in finite fields without derivated evaluation
- On the scalar complexity of Chudnovsky\(^2\) multiplication algorithm in finite fields
- ANTS XIII. Proceedings of the thirteenth algorithmic number theory symposium, University of Wisconsin-Madison, WI, USA, July 16--20, 2018
- On the tensor rank of multiplication in any extension of \(\mathbb F_2\)
- On the bilinear complexity of the multiplication in small finite fields
- Elliptic periods for finite fields
- The Difference Between Consecutive Primes, II
- On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields
- On products and powers of linear codes under componentwise multiplication
- Shimura Modular Curves and Asymptotic Symmetric Tensor Rank of Multiplication in any Finite Field
- Finding Optimal Chudnovsky-Chudnovsky Multiplication Algorithms
- Torsion Limits and Riemann-Roch Systems for Function Fields and Applications
- Testers and their applications
- Shimura curves of genus at most two
- Finding Optimal Formulae for Bilinear Maps
- Families of curves over finite fields
- Multiplication of Polynomials over Finite Fields
- On the existence of dimension zero divisors in algebraic function fields defined over Fq
- Characterization of Division Algebras of Minimal Rank and the Structure of their Algorithm Varieties
- ALGEBRAICO-GEOMETRIC CODES
- Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
- On symmetric algorithms for bilinear forms over finite fields
- An Improved Lower Bound on Polynomial Multiplication
- Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves
- Some bilinear forms whose multiplicative complexity depends on the field of constants
- Algebras Having Linear Multiplicative Complexities
- On tame towers over finite fields
- Asymptotic bounds on frameproof codes
- New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
- Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm
- Asymptotic Bound for Multiplication Complexity in the Extensions of Small Finite Fields
- On some bounds for symmetric tensor rank of multiplication in finite fields
- Algorithmic Number Theory
- Algebraic complexities and algebraic curves over finite fields
This page was built for publication: On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
