Generalized Hamming weights of linear codes

1992 ◽  
Vol 38 (3) ◽  
pp. 1133-1140 ◽  
Author(s):  
T. Helleseth ◽  
T. Klove ◽  
O. Ytrehus
Keyword(s):  
Linear Codes ◽  
Generalized Hamming Weights ◽  
Hamming Weights

scholarly journals Generalized Hamming weights of three classes of linear codes

2017 ◽  
Vol 45 ◽  
pp. 341-354 ◽  
Author(s):  
Gaopeng Jian ◽  
Rongquan Feng ◽  
Hongfeng Wu
Keyword(s):  
Linear Codes ◽  
Generalized Hamming Weights ◽  
Hamming Weights

scholarly journals A polymatroid approach to generalized weights of rank metric codes

2020 ◽  
Vol 88 (12) ◽  
pp. 2531-2546
Author(s):  
Sudhir R. Ghorpade ◽  
Trygve Johnsen
Keyword(s):  
Linear Codes ◽  
General Notion ◽  
Generalized Hamming Weights ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Hamming Weights

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.

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