Abstract
We present some recently obtained constructions of quasi-perfect linear codes with small density arising from plane cubic curves defined over finite fields.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
N. Anbar and M. Giulietti, Bicovering arcs and complete caps from elliptic curves, J. Algebraic Combin., published online 25/10/2012, DOI: 10.1007/sl0801-012-0407-8.
N. Anbar, D. Bartoli, M. Giulietti and I. Platoni, Small complete caps from singular cubics, preprint.
G. D. Cohen, A. C. Lobstein and N. J. A. Sloane, Further results on the covering radius of codes, IEEE Trans. Inform. Theory 32(5) (1986), 680–694.
M. Giulietti, Small complete caps in Galois affine spaces, J. Algebraic Combin. 25(2) (2007), 149–168.
J. W. P. Hirschfeld, “Projective Geometries over Finite Fields”, Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1998.
B. Segre, Proprietà elementari relative ai segmenti ed alle coniche sopra un campo qualsiasi ed una congettura di Seppo Ilkka per il caso dei campi di Galois, Ann. Mat. Pura Appl. (4) 96 (1972), 289–337.
J. F. Voloch, On the completeness of certain plane arcs. II, European J. Combin. 11(5) (1990), 491–496.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2013 Scuola Normale Superiore Pisa
About this paper
Cite this paper
Giulietti, M. (2013). Quasi-perfect linear codes from singular plane cubics. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_37
Download citation
DOI: https://doi.org/10.1007/978-88-7642-475-5_37
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-474-8
Online ISBN: 978-88-7642-475-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)