一类5维q元线性码重量谱的确定  

Determination on a class of weight hierarchies of q-ary linear codes of dimension 5

作　　者：王丽君[1] 陈文德[2] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074 [2]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,北京100190

出　　处：《科学通报》2011年第25期2150-2155,共6页Chinese Science Bulletin

基　　金：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)

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.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, in which we find new necessary conditions of weight hierarchies of 5-dimensional codes in class V, and classify the weight hierarchies of 5-dimensional codes in class V into two subclass,and advance subspace set method, and determine almost all the weight hierarchies of q-ary linear codes of dimension 5 in class V. It open the way for the remaining three class of weight hierarchies of 5-dimensional codes, and break through the difficulty. Furthermore, new necessary conditions show that original necessary conditions of weight hierarchies are not enough. We need to develop further new necessary conditions, in order to attack and solve problems of dimension k.

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 

分 类 号：O157.4[理学—数学]