Bicovering arcs and small complete caps from elliptic curves

Nurdagül Anbar Meidl, Massimo Giulietti

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Bicovering arcs in Galois affine planes of odd order are a powerful tool for the construction of complete caps in spaces of arbitrarily higher dimensions. The aim of this paper is to investigate whether the arcs contained in elliptic cubic curves are bicovering. As a result, bicovering k-arcs in AG(2,q) of size k≤q/3 are obtained, provided that q−1 has a prime divisor m with 7<m<(1/8)q 1/4. Such arcs produce complete caps of size kq (N−2)/2 in affine spaces of dimension N≡0(mod4). When q=p h with p prime and h≤8, these caps are the smallest known complete caps in AG(N,q), N≡0(mod4).
Original languageEnglish
JournalJournal of Algebraic Combinatorics
Volume38
Issue number2
Pages (from-to)371-392
ISSN0925-9899
Publication statusPublished - 2013
Externally publishedYes

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