Geodesic
Bicovering ARCS and small complete caps from elliptic curves
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 371-392.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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$\leq $q/3 are obtained, provided that q - 1 has a prime divisor m with 7(1/8)q $^{1/4}$. Such arcs produce complete caps of size kq $^{(N - 2)/2}$ in affine spaces of dimension N$\equiv 0(mod4)$. When q=p $^{ h }$ with p prime and h$\leq 8$, these caps are the smallest known complete caps in $AG(N,q)$, N$\equiv 0(mod4)$.
Keywords: Galois affine spaces, bicovering arcs, complete caps, quasi-perfect codes, elliptic curves 
@article{JAC_2013__38_2_a5,
     author = {Anbar, Nurdag\"ul and Giulietti, Massimo},
     title = {Bicovering {ARCS} and small complete caps from elliptic curves},
     journal = {Journal of Algebraic Combinatorics},
     pages = {371--392},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a5/}
}
TY  - JOUR
AU  - Anbar, Nurdagül
AU  - Giulietti, Massimo
TI  - Bicovering ARCS and small complete caps from elliptic curves
JO  - Journal of Algebraic Combinatorics
PY  - 2013
SP  - 371
EP  - 392
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a5/
LA  - en
ID  - JAC_2013__38_2_a5
ER  - 
%0 Journal Article
%A Anbar, Nurdagül
%A Giulietti, Massimo
%T Bicovering ARCS and small complete caps from elliptic curves
%J Journal of Algebraic Combinatorics
%D 2013
%P 371-392
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a5/
%G en
%F JAC_2013__38_2_a5
Anbar, Nurdagül; Giulietti, Massimo. Bicovering ARCS and small complete caps from elliptic curves. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 371-392. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a5/