Linear codes with few weights have applications in cryptography, association schemes, designs, strongly regular graphs, finite group theory, finite geometries, and secret sharing schemes, among other disciplines. Two-weight linear codes are particularly interesting because they are closely related to objects in different areas of mathematics such as strongly regular graphs, 3-rank permutation groups, ovals, and arcs. There exist techniques to construct linear codes with few weights, for example, the systematic exposition by Calderbank and Kantor (Bull Lond Math Soc 18(2):97–122, 1986). Ding et al., (World Sci, pp 119–124, 2008) and (IEEE Trans Inf Theory 61(11):5835–5842, 2015) constructed few-weight codes using the trace function and Tonchev et al. (Algorithms, 12(8), 2019) generalized Ding’s construction. In this paper, we present an elementary way to get two- and three-weight codes from simplex codes and antipodal linear codes. An interesting application is the construction of uniformly packed linear codes from two-weight codes and quaternary quasi-perfect linear codes from three-weight codes.

具有少量权重的线性码在密码学、关联方案、设计、强正则图、有限群论、有限几何和秘密共享方案等学科中有应用。二权线性码特别有趣，因为它们与不同数学领域的对象密切相关，例如强正则图、3 秩置换群、椭圆和弧。存在构造具有少量权重的线性码的技术，例如 Calderbank 和 Kantor 的系统阐述 (Bull Lond Math Soc 18(2):97–122, 1986)。Ding et al., (World Sci, pp 119–124, 2008) 和 (IEEE Trans Inf Theory 61(11):5835–5842, 2015) 使用跟踪函数和 Tonchev et al. 构建了少量权重代码。(Algorithms, 12(8), 2019) 概括了丁的构造。在本文中，我们提出了一种从单纯形码和对映线性码获得二重和三重码的基本方法。一个有趣的应用是从二权码构建均匀打包的线性码和从三权码构建四元准完美线性码。