| 一类5维q元线性码重量谱的确定 |
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| 引用本文： | 王丽君,陈文德.一类5维q元线性码重量谱的确定[J].科学通报,2011,56(25):2150-2155. |
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| 作者姓名： | 王丽君 陈文德 |
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| 作者单位： | 中南民族大学数学与统计学学院;中国科学院数学与系统科学研究院系统控制实验室与信息安全中心; |
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| 基金项目： | 中南民族大学中央高校基本科研业务费专项资金资助项目(CZQ10007) |
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| 摘 要： | “确定一般线性码的所有可能的重量谱”是通信系统中提出的一个有重要科学意义的基本理论问题. 但当k 或q 稍大时, 对于k 维q 元码, 这是不可能的, 问题的合理提法修改成: “确定k 维q 元一般线性码几乎所有的重量谱”. 基于有限射影几何方法, 本文研究V 类5 维q 元线性码, 文中找出了V 类5 维码的重量谱的新必要条件, 把V 类5 维码的重量谱分为两个子类,并发展改进了“子空间集法”, 从而确定了V 类5 维q 元线性码几乎所有的重量谱. 这为确定5维中剩下的3 类重量谱开辟了道路, 突破了难点. 同时, 新必要条件说明原来k 维码重量谱的必要条件是不够的, 需要研究出进一步的新必要条件, 才能攻击与解决k 维难题.
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| 关 键 词： | 重量谱 5 维q 元线性码 差序列 有限射影几何 子空间集 |
| 收稿时间： | 2011-05-23 |
Determination on a class of weight hierarchies of q-ary linear codes of dimension 5 |
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| WANG LiJun & CHEN WenDe College of Mathematics , Statistics,South-Central University for Nationalities,Wuhan ,China, Laboratory of Systems , Control , Information Security Center.Determination on a class of weight hierarchies of q-ary linear codes of dimension 5[J].Chinese Science Bulletin,2011,56(25):2150-2155. |
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| Authors: | WANG LiJun & CHEN WenDe College of Mathematics Statistics South-Central University for Nationalities Wuhan China Laboratory of Systems Control Information Security Center |
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| Institution: | WANG LiJun1 & CHEN WenDe2 1 College of Mathematics and Statistics,South-Central University for Nationalities,Wuhan 430074,China,2 Laboratory of Systems and Control and Information Security Center,Institute of Systems Science,Chinese Academy of Sciences,Beijing 100190 |
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| Abstract: | To determine all possible weight hierarchies of general linear codes is a basic theory having important scientific significance raised in the communication system. But when k or q is larger, it is impossible for q-ary linear codes of dimension k. Reasonable formulation of the problem is modified: to determine almost all the weight hierarchies of q-ary general linear codes of dimension k. Based on the finite projective geometry method, q-ary linear codes of dimension 5 in class V are studied in this paper, i... |
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| Keywords: | q-ary linear codes of dimension 5 deference sequence finite projective geometry subspace set method |
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