Generalized Hamming weights of codes over the $\mathcal{GH}$ curve

Alonso sepúlveda Castellanos

doi:10.3934/amc.2017006

Article Contents

2017, Volume 11, Issue 1: 115-122. Doi: 10.3934/amc.2017006

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Generalized Hamming weights of codes over the $\mathcal{GH}$ curve

Alonso sepúlveda Castellanos

Universidade Federal de Uberlândia, Campus Santa Mônica, CEP 38.408-100, Av. Joao Naves de Avila, 2121, Uberlandia-MG, Brazil

Received: May 31, 2015

Revised: January 31, 2016

Published: May 2017

The author would like to thank FAPEMIG by support

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Abstract

In this work, we studied the generalized Hamming weights of algebraic geometric Goppa codes on the $\mathcal{GH}$ curve. Especially, exact results on the second generalized Hamming weight are given for almost all cases. Furthermore, we apply the results obtained to show an example where the weight hierarchy characterizes the performance of the $\mathcal{GH}$ codes on a noiseless communication channel.

Keywords:

Generalized Hamming weights,
$\mathcal{GH}$ curve.

Mathematics Subject Classification: Primary: 14H55; Secondary: 11G20, 14G50.

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