New Lower Bounds on the Generalized Hamming Weights of AG Codes

Bras-Amoros M.; Lee K.; Vico-Oton A.

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New Lower Bounds on the Generalized Hamming Weights of AG Codes

机译：AG码的广义汉明权重的新下界

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摘要

A sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized. Then, the result is used, through the so-called Feng–Rao numbers, to bound the generalized Hamming weights of algebraic-geometry codes. This is further developed for Hermitian codes and the codes on one of the Garcia–Stichtenoth towers, as well as for some more general families.

机译：给出了不属于数值半群的理想值的最大整数的尖锐上限，并描述了达到该极限的理想值。然后，通过所谓的Feng-Rao数，将结果用于绑定代数几何代码的广义汉明权。这是针对Hermitian代码以及Garcia–Stichtenoth塔之一以及其他一些普通家庭的代码而进一步开发的。

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来源
《Information Theory, IEEE Transactions on》 |2014年第10期|5930-5937|共8页
作者
Bras-Amoros M.; Lee K.; Vico-Oton A.;
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作者单位

Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Tarragona, Catalonia, Spain;

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原文格式 PDF
正文语种 eng
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关键词
Conductors; Erbium; Hamming weight; Linear codes; Poles and towers; Upper bound; AG code; Feng-Rao number; Garcia-Stichtenoth towers; Hermitian codes; Numerical semigroup; generalized Hamming weights; ideal of a semigroup; isometry-dual sets of AG codes; order bound;

机译：导体;铒;汉明重量;线性代码;杆和塔;上限;AG代码;凤饶号;Garcia-Stichtenoth塔;埃尔米特密码;数值半群;广义汉明权重;半群的理想二维等距的AG代码集;订单约束;

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专利

1. Bounds for generalized Hamming weights of general AG codes [J] . Lee Kwankyu Finite fields and their applications . 2015,第jula期

机译：一般AG码的广义汉明权重的界限
2. Some bounds for the relative generalized Hamming weights of some evaluation codes [J] . Universitatea "Ovidius" Constanta. Analele. Seria Matematica . 2016,第2016期

机译：一些评估码的相对广义汉明权重的一些界
3. An improved Serre bound for elementary Abelian extensions of F/sub q/(x) and the generalized Hamming weights of duals of BCH codes [J] . Mereno O., Pedersen J.P. IEEE Transactions on Information Theory . 1998,第3期

机译：F / sub q /（x）的基本阿贝尔扩展和BCH码对偶的广义汉明权重的改进Serre界
4. A new approach to determine a lower bound of generalized Hamming weights using an improved Bezout theorem [C] . Gui-Liang Feng, Rao, T.R.N. . 1995

机译：一种使用改进的Bezout定理确定广义汉明权重下界的新方法
5. GENERALIZED WEIGHTS FOR LINEAR CODES. [D] . GOLDBERG, DONALD YALE. 1978

机译：线性编码的广义权重。
6. Generalized DNA Barcode Design Based on Hamming Codes [O] . Leonid V. Bystrykh 2009

机译：基于汉明码的广义DNA条形码设计
7. New Lower Bounds on the Generalized Hamming Weights of AG Codes [O] . Bras-Amorós, Maria, Lee, Kwankyu, Vico-Oton, Albert 2017

机译：aG代码广义Hamming权的新下界
8. Generalized Hamming Weights of Convolutional Codes [R] . Rosenthal, J., York, E. V. 1995

机译：卷积码的广义Hamming权重

New Lower Bounds on the Generalized Hamming Weights of AG Codes

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