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Kissing number of codes: A survey

Abstract : The kissing number of a code is the average number of pairs of codewords at minimum distance from each other. It has fundamental applications in determining codes performances. Besides, a recent interest has arisen from the field of side- channel analysis of algorithms handling sensitive information (e.g., cryptographic keys). Namely, when code-base masking protections are applied, their performance in terms of attacker’s signal-to-noise ratio or mutual information is proportional to the kissing number of the masking code. Therefore the kissing number is also a security metric for a given minimum distance in side-channel protected implementation, as it is in codes performance evaluation. It is known exactly for some classical families of codes. To estimate it in general, two types of bounds are given. Linear programming, either numerically or by the polynomial method is the most versatile and the more precise. Spectral graph theory provides bounds on the multiplicity of the subdominant eigenvalue that are easier to state.
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https://hal.telecom-paris.fr/hal-03718730
Contributeur : Olivier Rioul Connectez-vous pour contacter le contributeur
Soumis le : vendredi 12 août 2022 - 13:01:16
Dernière modification le : jeudi 18 août 2022 - 10:43:57

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  • HAL Id : hal-03718730, version 1

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Yi Liu, Wei Cheng, Olivier Rioul, Sylvain Guilley, Patrick Solé. Kissing number of codes: A survey. VIASM. Coding Theory and applications (tentative title), Springer, inPress, Lecture Notes in Mathematics. ⟨hal-03718730⟩

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