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Characterizations of o-polynomials by the Walsh transform

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Claude Carlet, Sihem Mesnager

Information Theory · Submitted 12 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this note, we characterize o-polynomials by the Walsh transform of the associated vectorial functions.

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arXiv ID1709.03765 (version 1)
Pith IDVQLBKSN3, Pith's permanent record of this paper and its review
CitationClaude Carlet, Sihem Mesnager. "Characterizations of o-polynomials by the Walsh transform." arXiv:1709.03765 (2017). https://pith.science/paper/VQLBKSN3
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,929 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The notion of o-polynomial comes from finite projective geometry. In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial Boolean functions, semi-bent functions and to construct good linear codes. In this note, we characterize o-polynomials by the Walsh transform of the associated vectorial functions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The notion of o-polynomial comes from finite projective geometry. background 1.00 0.04 0.02 asserted 1.00
s1 In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial Boolean functions, semi-bent functions and to construct good linear codes. background 1.00 0.05 0.03 asserted 1.00
s2 In this note, we characterize o-polynomials by the Walsh transform of the associated vectorial functions. contribution 1.00 0.92 0.83 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The notion of o-polynomial comes from finite projective geometry. In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial Boolean functions, semi-bent functions and to construct good linear codes. In this note, we characterize o-polynomials by the Walsh transform of the associated vectorial functions.

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