New binary optimal LCD codes using heuristic embedding

2026-09-02

AI Summary

本文通过基于贪心算法的启发式框架，构建了二进制最优LCD码，发现了14个新的最优LCD码。

Abstract

In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found $14$ optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.

Problem

• binary optimal LCD codes
• short LCD embeddings
• heuristic frameworks

Innovation

• heuristic framework
• greedy algorithm
• LCD embedding
• binary optimal LCD codes