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Designs, Codes and Cryptography

Erschienen in:

01.12.2014

Any network code comes from an algebraic curve taking osculating spaces

verfasst von: Edoardo Ballico

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2014

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Abstract

In this note we prove that every network code over \(\mathbb{F }_q\) may be realized taking some of the osculating spaces of a smooth projective curve.

Vorheriger Artikel Full analysis of PRINTcipher with respect to invariant subspace attack: efficient key recovery and countermeasures

Nächster Artikel Erratum to: On the support designs of extremal binary doubly even self-dual codes

Bollobas B.: Combinatorics. Cambridge University Press, Cambridge (1986).

Chou P.A., Wu Y., Jain K.: Practical network coding. In: Allerton Conference on Communication, Control, and Computing (2003).

Hansen J.P.: Equidistant Linear Network Codes with Maximal Error-Protection from Veronese Varieties. Lect. Notes in Computer Science. Springer (2013, to appear). arXiv:1207.2083.

Hansen J.P.: Osculating Spaces of Varieties and Linear Network Codes. arXiv:1210.7961v1 (2012).

Hirschfeld J W.P., Korchmáros G., Torres, F.: Algebraic curves over a finite field. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2008).

Ho T., Médard M., Koetter R., Karger D.R., Effros M., Shi J., Leong B.: A random linear network coding approach to multicast. IEEE Trans. Inform. Theory 52(10), 4413–4430 (2006).

Koetter R., Kschischang F.R.: Coding for errors and erasures in network coding. IEEE Trans. Inform. Theory 54(8), 3579–3591 (2008).

Laksov D.: Wronskians and Plücker formulas for linear systems on curves. Ann. Scient. École Norm. Sup. 17, 565–579 (1984).

Li S.-Y.R., Yeung R.W., Chai N.: Linear network coding. IEEE Trans. Inform. Theory 49(2), 371–381 (2003).

10.

Pellikann R., Shen B.-Z., van Wee G.J.M.: Which linear codes are algebraic–geometric? IEEE Trans. Inform. Theory 37(3), 583–602 (1991).

11.

Poonen B.J.: Bertini theorems over finite fields. Ann. Math. 160(3), 1099–1127 (2004).

12.

Poonen B.J.: Smooth hypersurface sections containing a given subscheme over a finite field. Math. Res. Lett. 15(2), 265–271 (2008).

13.

Trautmann A.-L., Manganiello F., Rosenthal J.: Orbit codes—a new concept in the area of network coding. In: Theory, Information Workshop (ITW), 2010 IEEE, Dublin, Ireland, pp. 1–4 (2010).

Titel: Any network code comes from an algebraic curve taking osculating spaces
verfasst von: Edoardo Ballico
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9841-4

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Any network code comes from an algebraic curve taking osculating spaces

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