Title: Kerdock codes and around Author: Kateřina Teplá Department: Department of algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of algebra Abstract: Kerdock codes form a family of nonlinear codes, that contains more codewords than any known linear code with the same parameters. The main goal of this thesis is a connection of Kerdock codes with other areas of mathematics, mainly orthogonal geometry, combinatorics and cryptogra- phy. It describes theory of symplectic and quadratic forms on vector spaces of characteristic 2 and its relationship to Kerdock codes. Then it is pro- ven, that codewords of Kerdock code of constant weight form combinatorial 3-design. Finally usage of Kerdock codes in construction of Boolean bent functions and t-resilient functions, that are basis of many cryptographic pri- mitives, is analysed. Keywords: Kerdock code, Kerdock set, t-design, resilient function 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:313896 |
| Date | January 2012 |
| Creators | Teplá, Kateřina |
| Contributors | Drápal, Aleš, Šťovíček, Jan |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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