Improvements on Generalized Hamming Weights of Some Trace Codes

The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. In this paper, some results are presented on the estimates of generalized Hamming weights of cyclic codes, which connect their corresponding trace codes.

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Generalized Hamming weights of trace codes

IEEE Transactions on Information Theory ◽

10.1109/18.312185 ◽

1994 ◽

Vol 40 (2) ◽

pp. 554-558 ◽

Cited By ~ 24

Author(s):

H. Stichtenoth ◽

C. Voss

Keyword(s):

Generalized Hamming Weights ◽

Trace Codes ◽

Hamming Weights

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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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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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