一类Reed-Muller型码的广义Hamming重量
On the generalized Hamming weights of certain Reed-Muller-type codes
摘要：
Beelen和M.仿射码的第$r$广义汉明重量的Datta。利用这个组合公式，我们给出了一个计算一类仿射码的$r$阶广义Hamming重量的简单公式.若$\mathbb{X}$是有限域上的一组投射点，则根据$\mathbb{X}$上相应的投射Reed-Muller型码及其对偶码的基本参数和广义Hamming重量，确定了$\mathbb{X}$上Veronese型码及其对偶码的基本参数和广义Hamming重量.
英文摘要：
There is a nice combinatorial formula of P. Beelen and M. Datta for the $r$-th generalized Hamming weight of an affine cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the $r$-th generalized Hamming weight for a family of affine cartesian codes. If $\mathbb{X}$ is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on $\mathbb{X}$ and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed--Muller-type codes on $\mathbb{X}$ and their dual codes.
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