Abstract
In this paper we construct functional codes from Denniston maximal arcs. For \(q=2^{4\ell +2}\) we obtain linear codes with parameters \([(\sqrt{q}-1)(q+1),5,d]_q\) where \(\lim _{q \rightarrow +\infty } d=(\sqrt{q}-1)q-\sqrt{q}\). We also find for \(q=16,32\) a number of linear codes which appear to have larger minimum distance with respect to the known codes with same length and dimension.
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Acknowledgements
The first two authors were supported in part by Ministry for Education, University and Research of Italy (MIUR) (Project PRIN 2012 “Geometrie di Galois e strutture di incidenza”) and by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The first author carried out this research within the project “Progetto Codici correttori di errori”, supported by Fondo Ricerca di Base, 2015, of Università degli Studi di Perugia. The second author carried out this research within the project “Progetto Geometrie di Galois, Curve Algebriche su campi finiti e loro Applicazioni”, supported by Fondo Ricerca di Base, 2015, of Università degli Studi di Perugia.
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Bartoli, D., Giulietti, M. & Montanucci, M. Linear codes from Denniston maximal arcs. Des. Codes Cryptogr. 87, 795–806 (2019). https://doi.org/10.1007/s10623-018-0515-0
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DOI: https://doi.org/10.1007/s10623-018-0515-0