Skip to Main content Skip to Navigation
New interface
Journal articles

Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields

Abstract : We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number 5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2 attaining the Drinfeld-Vladuts bound and on the descent of these families to the definition field Fp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (Funct Approx Commmentarii Math, 55(2):177-197, 2016).
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02115440
Contributor : Aigle I2m Connect in order to contact the contributor
Submitted on : Tuesday, April 30, 2019 - 12:00:17 PM
Last modification on : Friday, January 7, 2022 - 9:52:02 AM

Links full text

Identifiers

Collections

Citation

Stéphane Ballet, Alexey Zykin. Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields. Designs, Codes and Cryptography, 2019, 87 (2-3), pp.517-525. ⟨10.1007/s10623-018-0560-8⟩. ⟨hal-02115440⟩

Share

Metrics

Record views

41