Ⅵ-5类5维q元线性码的汉明重量的研究

中文摘要: 针对高维数线性码的汉明重量谱确定的困难性，为了解决维数为5的一般线性码的几乎所有的汉明重量谱的确定问题，运用有限射影几何的方法，通过将重量谱与差序列之间的一一对应关系，将确定重量谱问题转化为确定差序列问题；通过对不同情况下差序列的构造，证明了Ⅵ类中的第5个子类的必要条件是几乎充分的，从而确定了Ⅵ-5类中的几乎所有的差序列，即几乎所有的汉明重量谱。
Abstract:The method of finite project geometry was used to determine almost all weight hierarchies of the VI-5 subclass weight hierarchies of q-ary linear codes with dimension 5.For the one-to-one correspondence relationship between Hamming weight hierarchy and difference sequence,the determination of weight hierarchy can be converted into the determination of difference sequence.By constructing difference sequences under several different conditions,the necessary condition of the VI-5 class can be proved almost sufficient.So almost all weight hierarchies of the VI-5 class were determined.