This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Then we show that the linear codes spanned by the rows of these incidence matrices are subcodes of the 4-th order generalized Reed-Muller codes and also hold 2-designs. Finally, we determine the dimension and develop a lower bound on the minimum distance of the ternary linear codes.

中文翻译：

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2设计的线性码作为广义Reed-Muller码的子码

本文致力于由埃尔米特函数定义的仿射不变三元代码。我们首先计算由这些三态码的最小权重码字支持的2种设计的入射矩阵。然后我们证明，这些入射矩阵的行所跨越的线性码是4阶广义Reed-Muller码的子码，并且还具有2个设计。最后，我们确定尺寸并在三元线性编码的最小距离上确定一个下限。