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 $k \geq 2$ be an integer, define $S_{t}^{k} := {(a, b) \in Z^{2} | 0 \leq a, b \leq 2^{k} - 2, a + b \equiv t (mod 2^{k} - 1), \w (a) + \w (b) \leq k - 1},$ where $t \in Z, 1 \leq t \leq 2^{k} - 2$ . This paper gives the upper bound of cardinality of $S_{t}^{k}$ when $\w (t) \leq 10$ , 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},
      url = {https://eprint.iacr.org/2020/227}
}

Paper 2020/227

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

Abstract

Metadata

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