Bibak, Khodakhast Kapron, Bruce M. Srinivasan, Venkatesh
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...

Rodgers, Morgan
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} ...

Charpin, Pascale Langevin, Philippe
Published in
Designs, Codes and Cryptography

Carrier, Kevin Tillich, Jean-Pierre
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...

Ballet, Stéphane Zykin, Alexey
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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}$$...

Solov’eva, Faina Augot, Daniel Johansson, Thomas Minier, Marine Zinoviev, Victor
Published in
Designs, Codes and Cryptography

Ihringer, Ferdinand Meagher, Karen
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.

Cardinali, Ilaria Lavrauw, Michel Metsch, Klaus Pott, Alexander
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Designs, Codes and Cryptography

Shi, Minjia Liu, Yan Randriam, Hugues Sok, Lin Solé, Patrick
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...

Boura, Christina Canteaut, Anne Jean, Jérémy Suder, Valentin
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} ...