In this paper all the parameters in the conditions of rather comparatively larger probability of the value of n, have been discussed. In this extended range \(\upmu\) < n \(\le\) \(4\upmu\), the relation between existence of vector v(S) having the lowest weight in the coset RM_m + v(S), and different values of r and d, have been analyzed. The relation between the number (\(\tau\)) of vectors having lowest weight in RM_m + v(S) and various values of n, r, and d have been analyzed; and the corresponding values of \(\tau\) have been found. Also, the number of vectors (t) with lowest weight d for various values of d depending upon different quantities constituting the values of n and µ, has been found, n lying in extended range. All this is aimed at analyzing and improving the error-correcting-capacity of Reed–Muller code (first-order). Efforts are made to discuss the validity of the extended length of code and error-correcting-capacity of such a code of increased length.

在本文中，已经讨论了在n值具有相对较大概率的条件下的所有参数。在该扩展范围\（\ upmu \） <n \（\ le \） \（4 \ upmu \）中，向量v（S）的存在与同集RM _m  + v（S）中权重最低的关系，并且分析了r和d的不同值。分析了RM _m  + v（S）中权重最低的向量的数量（\（\ tau \））与n，r和d的各种值之间的关系；以及\（\ tau \）的对应值被发现。而且，已经发现对于不同的d值，根据构成n和μ的值的不同量，具有最小权重d的向量（t）的数量，n处于扩展范围内。所有这些旨在分析和提高Reed-Muller码（一阶）的纠错能力。努力讨论延长的代码长度的有效性和这种增加长度的代码的纠错能力。