Irreducible compositions of degree two polynomials over finite fields have regular structure
Let q be an odd prime power and D be the set of irreducible polynomials in Fq[x] which can be written as a composition of degree two polynomials. In this paper we prove that D has a natural regular structure by showing that there exists a finite automaton having D as accepted language. Our method is...
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| Format: | Journal article |
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Oxford University Press
2018
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| _version_ | 1797059926050209792 |
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| author | Ferraguti, A Micheli, G Schnyder, R |
| author_facet | Ferraguti, A Micheli, G Schnyder, R |
| author_sort | Ferraguti, A |
| collection | OXFORD |
| description | Let q be an odd prime power and D be the set of irreducible polynomials in Fq[x] which can be written as a composition of degree two polynomials. In this paper we prove that D has a natural regular structure by showing that there exists a finite automaton having D as accepted language. Our method is constructive. |
| first_indexed | 2024-03-06T20:10:59Z |
| format | Journal article |
| id | oxford-uuid:2a8d21ac-7a44-4d38-a43f-7d9eb0347903 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:10:59Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:2a8d21ac-7a44-4d38-a43f-7d9eb03479032022-03-26T12:25:40ZIrreducible compositions of degree two polynomials over finite fields have regular structureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a8d21ac-7a44-4d38-a43f-7d9eb0347903Symplectic Elements at OxfordOxford University Press2018Ferraguti, AMicheli, GSchnyder, RLet q be an odd prime power and D be the set of irreducible polynomials in Fq[x] which can be written as a composition of degree two polynomials. In this paper we prove that D has a natural regular structure by showing that there exists a finite automaton having D as accepted language. Our method is constructive. |
| spellingShingle | Ferraguti, A Micheli, G Schnyder, R Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title | Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title_full | Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title_fullStr | Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title_full_unstemmed | Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title_short | Irreducible compositions of degree two polynomials over finite fields have regular structure |
| title_sort | irreducible compositions of degree two polynomials over finite fields have regular structure |
| work_keys_str_mv | AT ferragutia irreduciblecompositionsofdegreetwopolynomialsoverfinitefieldshaveregularstructure AT michelig irreduciblecompositionsofdegreetwopolynomialsoverfinitefieldshaveregularstructure AT schnyderr irreduciblecompositionsofdegreetwopolynomialsoverfinitefieldshaveregularstructure |