Abstract
It is shown that any projective bundle of \(\mathrm{PG}(2,q)\) gives rise to a \(q\)-ary \((6, q^{6}\) \(+2q^{2}+2q+1,4;3)\) subspace code.
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).
Bray J.N., Holt D.F., Roney-Dougal Derek, C.M.: The Maximal Subgroups of the Low-Dimensional Finite Classical Groups. London Mathematical Society Lecture Note Series, vol. 407. Cambridge University Press, Cambridge (2013).
Cannon J., Playoust C.: An introduction to MAGMA. University of Sydney, Sydney (1993).
Glynn D.G.: Finite projective planes and related combinatorial systems. Ph.D. thesis, Adelaide University (1978).
Glynn D.G.: On finite division algebras. J. Comb. Theory Ser. A. 44(2), 253–266 (1987).
Hirschfeld J.W.P.H.: 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.H.: Projective Geometries over Finite Fields. Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1998).
Honold T., Kiermaier M., Kurz S.: Optimal binary subspace codes of length \(6\), constant dimension \(3\) and minimum distance \(4\). arXiv:1311.0464v1, preprint.
Huppert B.: Endliche Gruppen, I. Die Grundlehren der Mathematischen Wissenschaften, Band 134. Springer, Berlin (1967).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L. Storme.
Rights and permissions
About this article
Cite this article
Cossidente, A., Pavese, F. On subspace codes. Des. Codes Cryptogr. 78, 527–531 (2016). https://doi.org/10.1007/s10623-014-0018-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-014-0018-6