Automorphisms and isomorphisms of some p-ary bent functions
| Autor: | Ulrich Dempwolff |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Lemma (mathematics)
Automorphism group Algebra and Number Theory Bent function 010102 general mathematics Bent molecular geometry 0102 computer and information sciences Automorphism 01 natural sciences Prime (order theory) Cohomology Combinatorics 010201 computation theory & mathematics Discrete Mathematics and Combinatorics 0101 mathematics Equivalence (measure theory) Mathematics |
| Zdroj: | Journal of Algebraic Combinatorics. 51:527-566 |
| ISSN: | 1572-9192 0925-9899 |
| DOI: | 10.1007/s10801-019-00884-9 |
| Popis: | In the predecessor to this paper Dempwolff (Comm Algebra 34(3):1077–1131, 2006), group-theoretic methods were used to solve automorphism and equivalence questions for (certain) ordinary bent functions, i.e., bent functions over \(\mathbb {F}_2\). Here, we consider the same problems for p-ary bent functions, p an odd prime and solve these questions for functions analogous to those which appear in Dempwolff (Comm Algebra 34(3):1077–1131, 2006). Although our general analysis is similar to the approach of Dempwolff (Comm Algebra 34(3):1077–1131, 2006), it turns out that the odd characteristic leads to simplifications: Often, the double derivative can be computed (cf. Lemma 2.10) and factorizations of the automorphism group (cf. Lemma 2.3) can be established resulting in restrictions for automorphisms and equivalence maps. |
| Databáze: | OpenAIRE |
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