Abstract
We show that extended cyclic codes over Fq with parameters [q+ 2 , 3 , q] , q= 2 m, determine regular hyperovals. We also show that extended cyclic codes with parameters [qt- q+ t, 3 , qt- q] , 1 < t< q, q is a power of t, determine (cyclic) Denniston maximal arcs. Similarly, cyclic codes with parameters [q2+ 1 , 4 , q2- q] are equivalent to ovoid codes obtained from elliptic quadrics in PG(3, q). Finally, we give simple presentations of Denniston maximal arcs in PG(2, q) and elliptic quadrics in PG(3, q).
Original language | English |
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Pages (from-to) | 2283-2294 |
Number of pages | 12 |
Journal | Designs, Codes, and Cryptography |
Volume | 89 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2021 |
Keywords
- Extended cyclic codes
- Hyperovals
- MDS codes
- Maximal arcs
- Ovoids
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Applied Mathematics