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papers

Publications (37)

cs.IT2009

Triple-Error-Correcting BCH-Like Codes

Carl Bracken, Tor Helleseth

The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance 7 with generator polynomial having zeros $I^\pm$ , $I^\pm^{3}$ and $I^\pm^{5}$ where $I^\pm$ is a primitiv…

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.IT2013

The Proof of Lin's Conjecture via the Decimation-Hadamard Transform

Honggang Hu, Shuai Shao, Guang Gong +1

In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their…

cs.IT2019

Cryptographically Strong Permutations from the Butterfly Structure

Kangquan Li, Chunlei Li, Tor Helleseth +1

In this paper, we present infinite families of permutations of $F_{2^{2 n}}$ with high nonlinearity and boomerang uniformity $4$ from generalized butterfly structures. Both…

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.IT2021

The Differential Spectrum of the Power Mapping $x^{p^{n} - 3}$

Haode Yan, Yongbo Xia, Chunlei Li +3

Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^{n} - 3}$ over $F_{p^{n}}$ has desirable differential properties, and its differential spectra for $p=2,\,…