On (2n/3-1)-Resilient (n,2)-Functions Научная публикация
| Журнал |
IEEE International Symposium on Information Theory - Proceedings
ISSN: 2157-8095 |
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| Вых. Данные | Год: 2019, Том: 2019, Страницы: 2957-2961 Страниц : 5 DOI: 10.1109/isit.2019.8849584 | ||
| Ключевые слова | Boolean function, resilient function, equitable partition, hypercube, Latin hypercubes, binary 1-perfect codes | ||
| Авторы |
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| Организации |
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Реферат:
A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy t≤2n/3-1; moreover, the (2n/3-1)-resilient (n,2)-functions correspond to the equitable partitions of the n-cube with the quotient matrix [[0,r,r,r],[r,0,r,r],[r,r,0,r],[r,r,r,0]], r=n/3. We suggest constructions of such functions and corresponding partitions, show connections with Latin hypercubes and binary 1-perfect codes, characterize the non-full-rank and the reducible functions from the considered class, and discuss the possibility to make a complete characterization of the class.
Библиографическая ссылка:
Krotov D.S.
On (2n/3-1)-Resilient (n,2)-Functions
IEEE International Symposium on Information Theory - Proceedings. 2019. V.2019. P.2957-2961. DOI: 10.1109/isit.2019.8849584 WOS Scopus РИНЦ OpenAlex
On (2n/3-1)-Resilient (n,2)-Functions
IEEE International Symposium on Information Theory - Proceedings. 2019. V.2019. P.2957-2961. DOI: 10.1109/isit.2019.8849584 WOS Scopus РИНЦ OpenAlex
Даты:
| Опубликована online: | 26 сент. 2019 г. |
Идентификаторы БД:
| Web of science: | WOS:000489100303012 |
| Scopus: | 2-s2.0-85073171511 |
| РИНЦ: | 41690863 |
| OpenAlex: | W2976940018 |