Projective Nested Cartesian Codes
Projective Nested Cartesian Codes
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投影嵌套笛卡尔代码
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Hiram H. López
中科院分区：
文献类型：
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作者：
C. Carvalho;V. Neumann;Hiram H. López
本文介绍了一类新的码族，称为射影嵌套笛卡儿码。它们是通过对PN(FQ)文档类[12pt]{minimum}usepackage{amsath}usepackage{wa ysym}usepackage{amssymb}usepackage{amsbsy}usepackage{masbsy}usepackage{upgreek}setlong{oddsidemarin}{-69pt}中的某个子集上的定次齐次多项式求值而得到的，例如在{Document}$mathbb{P}^n(mathbb{F}_q)$end{Document}中，它们可以看作是所谓的射影Reed-Muller码的推广。在一种特殊情况下(包括射影Reed-Muller码)，我们计算了这种码的长度和维数、最小距离的上界和精确的最小距离。最后给出了这些码的参数与仿射笛卡尔码参数之间的一些关系。
In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of Pn(Fq)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {P}^n(mathbb {F}_q)$$end{document}, and they may be seen as a generalization of the so-called projective Reed–Muller codes. We calculate the length and the dimension of such codes, an upper bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed–Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes.