Abstract
Using the geometry of quadrics of a projective plane \(\mathrm{PG}(2,q)\) a family of \((6,q^3(q^2-1)(q-1)/3+(q^2+1)(q^2+q+1),4;3)_q\) constant dimension subspace codes is constructed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baker, R.D., Brown, J.M.N., Ebert, G.L., Fisher, J.C.: Projective bundles. Bull. Belg. Math. Soc. Simon Stevin 1(3), 329–336 (1994)
Baker, R.D., Bonisoli, A., Cossidente, A., Ebert, G.L.: Mixed partitions of PG(5, \(q\)). Discrete Math. 208(209), 23–29 (1999)
Ballico, E., Cossidente, A., Siciliano, A.: External flats to varieties in symmetric product spaces over finite fields. Finite Fields Appl. 9(3), 300–309 (2003)
Bray, J.N., Holt, D.F., Roney-Dougal, C.M.: The Maximal Subgroups of the Low-dimensional Finite Classical Groups, London Mathematical Society Lecture Note Series 407. Cambridge University Press, Cambridge (2013)
Cannon, J., Playoust, C.: An Introduction to MAGMA. University of Sydney, Sydney (1993)
Cossidente, A., Pavese, F.: On subspace codes. Des. Codes Cryptogr. (to appear). doi:10.1007/s10623-014-0018-6
Figueroa, R.: A family of not \((V, l)\). Math. Z. 181(4), 471–479 (1982)
Glynn, D.G.: Finite Projective Planes and Related Combinatorial Systems, Ph.D. thesis, Adelaide University (1978)
Glynn, D.G.: On finite division algebras. J. Combin. Theory Ser. A 44(2), 253–266 (1987)
Honold, T., Kiermaier, M., Kurz, S.: Optimal binary subspace codes of length \(6\). Contemp. Math.-Am. Math. Soc. 632, 157–176 (2015)
Hirschfeld, J.W.P.: Projective Geometries over Finite Fields, Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1998)
Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1985)
Hirschfeld, J.W.P., Thas, J.A.: General Galois Geometries, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1991)
Huppert, B.: Endliche Gruppen, I. Die Grundlehren der Mathematischen Wissenschaften, Band 134 Springer, Berlin-New York (1967)
Steiner, J.: Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander. Reimer, Berlin (1832)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. W. P. Hirschfeld.
Rights and permissions
About this article
Cite this article
Cossidente, A., Pavese, F. Veronese subspace codes. Des. Codes Cryptogr. 81, 445–457 (2016). https://doi.org/10.1007/s10623-015-0166-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-015-0166-3