A binary code that has the parameters and possesses the main properties of the classical \(r\)th-order Reed–Muller code \(RM_{r,m}\) will be called an \(r\)th-order Reed–Muller like code and will be denoted by \(LRM_{r,m}\). The class of such codes contains the family of codes obtained by the Pulatov construction and also classical linear and \(\mathbb{Z}_4\)-linear Reed–Muller codes. We analyze the intersection problem for the Reed–Muller like codes. We prove that for any even \(k\) in the interval \(0\le k\le 2^{2\sum\limits_{i=0}^{r-1}\binom{m-1}{i}}\) there exist \(LRM_{r,m}\) codes of order \(r\) and length \(2^m\) having intersection size \(k\). We also prove that there exist two Reed–Muller like codes of order \(r\) and length \(2^m\) whose intersection size is \(2k_1 k_2\) with \(1\le k_s\le |RM_{r-1,m-1}|\), \(s\in\{1,2\}\), for any admissible length starting from 16.

具有参数并具有经典\(r\)次 Reed–Muller 代码\(RM_{r,m}\)的主要性质的二进制代码将被称为\(r\)次 Reed –Muller 类似代码，将用\(LRM_{r,m}\)表示。此类代码包含通过 Pulatov 构造获得的代码族以及经典线性和\(\mathbb{Z}_4\) -线性 Reed-Muller 代码。我们分析了类似 Reed-Muller 代码的交集问题。我们证明对于区间\(0\le k\le 2^{2\sum\limits_{i=0}^{r-1}\binom{m-1}{i中的任何偶数\(k\) }}\)存在\(LRM_{r,m}\)顺序代码\(r\)和长度\(2^m\)具有交集大小\(k\)。我们还证明了存在两个类似 Reed-Muller 的序码\(r\)和长度\(2^m\)，其交集大小为\(2k_1 k_2\)与\(1\le k_s\le |RM_{ r-1,m-1}|\) , \(s\in\{1,2\}\)，适用于从 16 开始的任何允许长度。