Extended cyclic codes, maximal arcs and ovoids

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)2283-2294
Number of pages12
JournalDesigns, Codes, and Cryptography
Volume89
Issue number10
DOIs
Publication statusPublished - Oct 2021

Keywords

  • Extended cyclic codes
  • Hyperovals
  • Maximal arcs
  • MDS codes
  • Ovoids

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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