T. Helleseth

collaborators

5 papers

cs.DM2025

Ternary Binomial and Trinomial Bent Functions in the Completed Maiorana-McFarland Class

Tor Helleseth, Alexander Kholosha, Niki Spithaki

Two classes of ternary bent functions of degree four with two and three terms in the univariate representation that belong to the completed Maiorana-McFarland class are found. Bino…

cs.IT2024

Determining the covering radius of all generalized Zetterberg codes in odd characteristic

Minjia Shi, Shitao Li, Tor Helleseth +1

For an integer $s \geq 1$ , let $C_{s} (q_{0})$ be the generalized Zetterberg code of length $q_{0}^{s} + 1$ over the finite field $\F_{q_0}$ of odd characteristic. Recently, Shi, Hell…

cs.CR2024

Further Investigation on Differential Properties of the Generalized Ness-Helleseth Function

Yongbo Xia, Chunlei Li, Furong Bao +2

Let $n$ be an odd positive integer, $p$ be a prime with $p \equiv 3 (mod 4)$ , $d_{1} = \frac{p ^{n} - 1}{2} - 1$ and $d_{2} = p^{n} - 2$ . The function defined by $f_u(x)=ux^{d_{1}}+x^{d_{…

cs.CR2024

An updated review on cross-correlation of m-sequences

Tor Helleseth, Chunlei Li

Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have…

cs.IT2024

Further Investigations on Nonlinear Complexity of Periodic Binary Sequences

Qin Yuan, Chunlei Li, Xiangyong Zeng +2

Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite…