generalized hamming weights
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2020 ◽  
Vol 88 (12) ◽  
pp. 2531-2546
Author(s):  
Sudhir R. Ghorpade ◽  
Trygve Johnsen

Abstract We consider the notion of a (q, m)-polymatroid, due to Shiromoto, and the more general notion of (q, m)-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martínez-Peñas and Matsumoto for relative generalized rank weights are derived as a consequence.


2020 ◽  
Vol 28 (1) ◽  
pp. 205-217
Author(s):  
Manuel González-Sarabia ◽  
Delio Jaramillo ◽  
Rafael H. Villarreal

AbstractThere is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If 𝕏 is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on 𝕏 and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed–Muller-type codes on 𝕏 and their dual codes.


2020 ◽  
Vol 343 (1) ◽  
pp. 111639
Author(s):  
José Martínez-Bernal ◽  
Miguel A. Valencia-Bucio ◽  
Rafael H. Villarreal

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1406
Author(s):  
Bras-Amorós

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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