The second generalized Hamming weight of certain Castle codes

Olaya-Leon Wilson; Granados-Pinzon Claudia

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The second generalized Hamming weight of certain Castle codes

机译：某些城堡码的第二个广义汉明权重

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摘要

We compute the bound on the second generalized Hamming weight for some AG codes coming from Castle curves. We consider those codes related to Weierstrass semigroups generated by two integers. Important codes as Hermitian, Norm-Trace and certain hyperelliptic codes belong to this class of codes. We obtain a simple characterization for the true values of the second generalized Hamming weight of all Hermitian codes.

机译：我们为来自Castle曲线的一些AG代码计算第二个广义汉明权重的界限。我们考虑那些与由两个整数生成的Weierstrass半群有关的代码。诸如Hermitian，Norm-Trace和某些超椭圆形代码之类的重要代码都属于此类代码。我们获得了所有厄米编码的第二个广义汉明权重的真实值的简单表征。

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来源
《Designs, Codes and Crytography》 |2015年第1期|81-87|共7页
作者
Olaya-Leon Wilson; Granados-Pinzon Claudia;
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作者单位

Univ Ind Santander, Escuela Matemat, Bucaramanga 678, Santander, Colombia;

Univ Ind Santander, Escuela Matemat, Bucaramanga 678, Santander, Colombia;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Error-correcting codes; AG codes; Castle codes; Generalized Hamming weights; Hermitian codes;

机译：纠错码;AG码;城堡码;广义汉明权重;厄密码;

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1. ON THE RELATIVE GENERALIZED HAMMING WEIGHTS OF LINEAR CODES AND THEIR SUBCODES [J] . ZIHUI LIU, JIE WANG, XIN-WEN WU SIAM Journal on Discrete Mathematics . 2011,第4期

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2. Weight Functions and Generalized Hamming Weights of Linear Codes [J] . D. Yu. Nogin Problems of information transmission . 2005,第2期

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3. Notes on generalized Hamming weights of some classes of binary codes [J] . Zihui Liu, Jinliang Wang Cryptography and Communications . 2020,第4期

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4. Relative Generalized Hamming Weights and Extended Weight Polynomials of Almost Affine Codes [C] . Trygve Johnsen, Hugues Verdure Coding theory and applications . 2017

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5. GENERALIZED WEIGHTS FOR LINEAR CODES. [D] . GOLDBERG, DONALD YALE. 1978

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7. Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes [O] . Nupur Patanker, Sanjay Kumar Singh 2021

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8. Generalized Hamming Weights of Convolutional Codes [R] . Rosenthal, J., York, E. V. 1995

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The second generalized Hamming weight of certain Castle codes

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