nach oben

Designs, Codes and Cryptography

Erschienen in:

01.10.2016

A generalization of Kung’s theorem

verfasst von: Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2016

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We give a generalization of Kung’s theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all \(i=k+1,\ldots ,n\), we give an upper bound on the smallest integer m such that there exist m codewords whose union of supports has cardinality at least i.

Vorheriger Artikel Complete weight enumerators of some linear codes and their applications

Ball S., Blokhuis A.: A bound for the maximum weight of a linear code. SIAM J. Discret. Math. 27(1), 575–583 (2013).

Britz T., Shiromoto K.: On the covering dimension of a linear code. arXiv:1504.02357 (2015).

Crapo H., Rota G.-C.: On the Foundation of Combinatorial Theory: Combinatorial Geometries (Preliminary Edition). MIT Press, Cambridge (1970).

Johnsen T., Roksvold J.N., Verdure H.: A Generalization of Weight Polynomials to Matroids. arXiv:1311.6291 (2013).

Jurrius R.: Weight enumeration of codes from finite spaces. Des. Codes Cryptogr. 63(3), 321–330 (2012).

Jurrius R.: Codes, arrangements, matroids, and their polynomial links. PhD thesis, Technische Universiteit Eindhoven. http://alexandria.tue.nl/extra2/734704 (2012).

Jurrius R., Pellikaan R.: Codes, arrangements and matroids. In: Algebraic Geometry Modeling in Information Theory. Series on Coding Theory and Cryptology, vol. 8, pp. 219–325. World Scientific Publishing, Hackensack (2013).

Kløve T.: Support weight distribution of linear codes. Discret. Math. 106(107), 311–316 (1992).

Kung, J.P.S.: Critical problems. In: Matroid Theory (Seattle, WA, 1995). Contemporary Mathematics, vol. 197, pp. 1–127. American Mathematical Society, Providence (1996).

10.

Wei V.K.: Generalized Hamming weights for linear codes. IEEE Trans. Inf. Theory 37(5), 1412–1418 (1991).

Titel: A generalization of Kung’s theorem
verfasst von: Trygve Johnsen
Keisuke Shiromoto
Hugues Verdure
Publikationsdatum: 01.10.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0139-6

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 1/2016

New infinite series of 2-designs over the binary and ternary field

A reduction of Semigroup DLP to classic DLP

Two classes of cyclic codes and their weight enumerator

Separating invertible key derivations from non-invertible ones: sequential indifferentiability of 3-round Even–Mansour

Graph-theoretic design and analysis of key predistribution schemes

A note on relative hemisystems of Hermitian generalised quadrangles