论文标题
2设计的线性代码作为扩展的广义芦苇毛刺代码的子代码
Linear Codes Of 2-Designs As Subcodes Of The Extended Generalized Reed-Muller Codes
论文作者
论文摘要
本文关注的是由Hermitian功能定义的仿射不变三元代码。我们计算了这些三元代码的最小重量编码器支持的2设计的发射率矩阵。这些发生率矩阵的行生成的线性代码是第4阶通用芦苇毛刺代码的扩展代码的子代码，它们还持有2个设计。最后，我们给出了这些线性代码的最小重量的尺寸和下限。
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear codes generated by the rows of these incidence matrix are subcodes of the extended codes of the 4-th order generalized Reed-Muller codes and they also hold 2-designs. Finally, we give the dimensions and lower bound of the minimum weights of these linear codes.
