Characterization and classification of optimal LCD codes

On the classification of quaternary optimal Hermitian LCD codes

We propose a method for a classification of quaternary Hermitian LCD codes having large minimum weights. As an example, we give a classification of quaternary optimal Hermitian LCD codes of dimension 3.

Classification of optimal quaternary Hermitian LCD codes of dimension $2$

Hermitian linear complementary dual codes are linear codes whose intersection with their Hermitian dual code is trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$.

Optimal Binary LCD Codes

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1964. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, cryptography, etc. In this paper, we prove some properties of binary LCD codes using their shortened and punctured codes. We also present some inequalities for the largest minimum weight $d_{LCD}(n,k)$ of binary LCD [n,k] codes for given length n and dimension k. Furthermore, we give two tables with the values of $…

二元帽与大维度LCD码

Caps and LCD Codes with Large Dimensions

研究通过建立线性互补双码与射影空间帽的关系，推导出最小距离至少为4的LCD码不存在性定理，并首次确定了码维7和8的最优最小距离。

学习最优二叉分类树的混合整数线性优化建模

Mixed integer linear optimization formulations for learning optimal binary classification trees

本文针对最优二叉分类树设计问题，提出四种混合整数线性优化建模（两种基于流、两种基于割），并与已有最强流建模进行理论比较，在13个公开数据集上验证了模型的可扩展性和双目标Pareto前沿方法的有效性。