A class of cyclotomic linear codes and their generalized Hamming weights

TL;DR

This paper introduces a new class of cyclotomic linear codes, providing formulas for their generalized Hamming weights, analyzing their weight distribution, and fully determining their weights in a specific case.

Contribution

It presents novel formulas for generalized Hamming weights of codes from defining sets and fully solves the weights for a particular case.

Findings

Derived formulas for generalized Hamming weights of codes from defining sets

Established a class of cyclotomic linear codes with calculable weights

Fully determined weights in a special case

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.