Published in Designs, Codes and Cryptography
In this paper, we first give explicit formulas for the number of solutions of unweighted linear congruences with distinct coordinates. Our main tools are properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions. Then, as an application, we derive an explicit formula for the number of codewords in the Varshamov–Tene...
Published in Designs, Codes and Cryptography
New examples of Cameron–Liebler line classes in PG(3, q) are given with parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{2}(q^2 -1)}$$\end{document} ...
Published in Designs, Codes and Cryptography
Published in Designs, Codes and Cryptography
We consider in this paper the problem of reconstructing a linear code from a set of noisy codewords. We revisit the algorithms that have been devised for solving this problem and show that by generalizing and mixing two approaches that have been proposed in this setting, we obtain a significantly better algorithm. It basically consists in setting u...
Published in Designs, Codes and Cryptography
We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$...
Published in Designs, Codes and Cryptography
Published in Designs, Codes and Cryptography
The original version of this article unfortunately contained a mistake. The authors incorrectly quoted Manickam-Miklós-Singhi (MMS) conjecture as “Miklós–Manickam–Singhi”. The correct term for the conjecture is Manickam–Miklós–Singhi.
Published in Designs, Codes and Cryptography
Published in Designs, Codes and Cryptography
We construct trace codes over Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document} based on Boolean functions and their support. The Lee weig...
Published in Designs, Codes and Cryptography
In this work, we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same difference distribution table (DDT). Next, we compare this notion to what we call the γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} ...
