Extended cyclic codes, maximal arcs and ovoids

Abdukhalikov K. Ho D.
October 2021 Springer

Designs, Codes, and Cryptography
2021 #89 Issue 10 2283 - 2294 pp.

We show that extended cyclic codes over F_q 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).

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

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