Curves with many points and multiplication complexity in any extension of \(\mathbb{F}_q\)
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Publication:1808846
DOI10.1006/ffta.1999.0255zbMath0953.11022OpenAlexW1998210995MaRDI QIDQ1808846
Publication date: 10 February 2000
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/ffta.1999.0255
Related Items (30)
An improvement of the construction of the D. V. and G. V. Chudnovsky algorithm for multiplication in finite fields ⋮ 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 ⋮ An improvement of bilinear complexity bounds in some finite fields. ⋮ On some bounds for symmetric tensor rank of multiplication in finite fields ⋮ Chudnovsky-type algorithms over the projective line using generalized evaluation maps ⋮ Tower of algebraic function fields with maximal Hasse-Witt invariant and tensor rank of multiplication in any extension of \(\mathbb{F}_2\) and \(\mathbb{F}_3\) ⋮ 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 ⋮ On the tensor rank of multiplication in any extension of \(\mathbb F_2\) ⋮ The equivariant complexity of multiplication in finite field extensions ⋮ 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. ⋮ On the tensor rank of the multiplication in the finite fields ⋮ 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 ⋮ A tower with non-Galois steps which attains the Drinfeld-Vladut bound ⋮ Trisymmetric multiplication formulae in finite fields ⋮ Effective arithmetic in finite fields based on Chudnovsky's multiplication algorithm ⋮ On multiplication in finite fields ⋮ On the bounds of the bilinear complexity of multiplication in some finite fields ⋮ On the construction of the asymmetric Chudnovsky multiplication algorithm in finite fields without derivated evaluation ⋮ On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields ⋮ On the bilinear complexity of the multiplication in small 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 ⋮ SINGULAR CURVES WITH LINE BUNDLES L DEFINED OVER ${\mathbb F}_q$ AND WITH H0(L) = H1(L) = 0 ⋮ Construction of asymmetric Chudnovsky-type algorithms for multiplication in finite fields ⋮ Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm ⋮ Quasi-optimal algorithms for multiplication in the extensions of \(\mathbb F_{16}\) of degree 13, 14 and 15
Cites Work
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- Algebraic function fields and codes
- On the complexity of multiplication in finite fields
- On multiplication in algebraic extension fields
- A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
- The genus of curves over finite fields with many rational points
- Lectures on the theory of algebraic functions of one variable
- Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves
- Abelian varieties over finite fields
- Algebraic complexities and algebraic curves over finite fields
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