Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes

Abstract In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX′(d) when X′ is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori Tn₁-1 and Tn₂-1.

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On the generalized Hamming weights of cyclic codes

IEEE Transactions on Information Theory ◽

10.1109/18.567719 ◽

1997 ◽

Vol 43 (1) ◽

pp. 299-308 ◽

Cited By ~ 7

Author(s):

H. Janwa ◽

A.K. Lal

Keyword(s):

Cyclic Codes ◽

Generalized Hamming Weights ◽

Hamming Weights

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Generalized Hamming weights of convolutional codes

Proceedings of 1995 IEEE International Symposium on Information Theory ◽

10.1109/isit.1995.531511 ◽

2002 ◽

Author(s):

J. Rosenthal ◽

E. Von York

Keyword(s):

Convolutional Codes ◽

Generalized Hamming Weights ◽

Hamming Weights

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Improvements on Generalized Hamming Weights of Some Trace Codes

Designs Codes and Cryptography ◽

10.1007/s10623-005-3394-0 ◽

2006 ◽

Vol 39 (2) ◽

pp. 215-231 ◽

Cited By ~ 4

Author(s):

Cem Güneri ◽

Ferruh Özbudak

Keyword(s):

Generalized Hamming Weights ◽

Trace Codes ◽

Hamming Weights

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Ideals of Numerical Semigroups and Error-Correcting Codes

Symmetry ◽

10.3390/sym11111406 ◽

2019 ◽

Vol 11 (11) ◽

pp. 1406

Author(s):

Bras-Amorós

Keyword(s):

Secret Sharing ◽

Error Correcting Codes ◽

Numerical Semigroups ◽

Secret Sharing Schemes ◽

List Decoding ◽

Generalized Hamming Weights ◽

Resilient Functions ◽

Weierstrass Semigroups ◽

Hamming Weights ◽

Dual Sequences

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

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