A class of cyclotomic linear codes and their generalized Hamming weights

Abstract

Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas to calculate their generalized Hamming weights. Lastly, we determine their weight distribution and generalized Hamming weights partially. Especially, we solved the generalized Hamming weights completely in one case.

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References in corpus (2)

• Complete Weight Enumerators of a Family of Three-Weight Linear Codes
• Generalized Hamming weights of three classes of linear codes

Cited by in corpus (4)

• Weight distributions and weight hierarchies of two classes of binary linear codes
• Weight hierarchy of a class of linear codes relating to non-degenerate quadratic forms
• Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes
• Weight hierarchies of a family of linear codes associated with degenerate quadratic forms