Report
Some hypersurfaces over finite fields, minimal codes and secret sharing schemes
| العنوان: | Some hypersurfaces over finite fields, minimal codes and secret sharing schemes |
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| المؤلفون: | Aguglia, Angela, Ceria, Michela, Giuzzi, Luca |
| المصدر: | Designs, Codes and Cryptography (2022) 90:1503-1519 |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Information Theory, Mathematics - Combinatorics, 94B05, 51E22, 94A60 |
| الوصف: | Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult. Here we investigate the properties of certain algebraic hypersurfaces over finite fields, whose intersection numbers with any hyperplane only takes a few values; these varieties give rise to $q$-divisible linear codes with at most $5$ weights. Furthermore, for $q$ odd these codes turn out to be minimal and we characterize the access structures of the secret sharing schemes based on their dual codes. Indeed, the secret sharing schemes thus obtained are democratic, that is each participant belongs to the same number of minimal access sets and can easily be described. Comment: 20 pages; fully revised version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10623-022-01051-1 |
| URL الوصول: | http://arxiv.org/abs/2105.14508 |
| رقم الانضمام: | edsarx.2105.14508 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10623-022-01051-1 |
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