Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in Galois Geometry often require a certain divisibility of the occurring weights. In this paper we present an algorithmic framework for the classification of linear codes over finite fields with restricted sets of weights. The underlying algorithms are based on lattice point enumeration and integer linear programming. We present new enumeration and non-existence results for projective two-weight codes, divisible codes, and additive $\mathbb{F}_4$-codes.

翻译：线性码在编码理论中处于核心地位，并广泛应用于数学的多个分支。出于纠错目的，最小汉明距离应尽可能大。与伽罗瓦几何应用相关的线性码通常要求码重满足特定的可整除性。本文提出一种算法框架，用于对有限域上具有受限权重集合的线性码进行分类。基础算法基于格点枚举与整数线性规划。针对射影二重码、可整除码以及加法$\mathbb{F}_4$码，我们给出了新的枚举结果与不存在性结论。