About the Tu-Deng Conjecture for $\w(t)$ Less Than or Equal to 10

Yindong Chen; Limin Lin; Chuliang Wei

Paper 2020/227

About the Tu-Deng Conjecture for $\w(t)$ Less Than or Equal to 10

Yindong Chen, Limin Lin, and Chuliang Wei

Abstract

Let $k \ge 2$ be an integer, define $$ S_t^k:=\Bigg\{(a,b)\in \mathbb{Z}^2\ \Big| \ { 0 \le a,b \le 2^{k}-2,\ a+b\equiv t ~(\text{mod} \ 2^k-1),\ \w(a)+\w(b)\le{k-1}}\Bigg\},$$ where $t \in \mathbb{Z}, 1 \le t \le 2^k-2$. This paper gives the upper bound of cardinality of $S_t^k$ when $\w(t)\le 10$, proving that a conjecture proposed by Tu and Deng in the case.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Tu-Deng Conjecture algebraic immunity Boolean function Hamming weight
Contact author(s): ydchen @ stu edu cn
History: 2020-02-21: received
Short URL: https://ia.cr/2020/227
License: CC BY

BibTeX

@misc{cryptoeprint:2020/227,
      author = {Yindong Chen and Limin Lin and Chuliang Wei},
      title = {About the Tu-Deng Conjecture for $\w(t)$ Less Than or Equal to 10},
      howpublished = {Cryptology ePrint Archive, Paper 2020/227},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/227}},
      url = {https://eprint.iacr.org/2020/227}
}