Self-orthogonal codes from plateaued functions and their applications in quantum codes and LCD codes
Abstract
Self-orthogonal codes have received great attention due to their important applications in quantum codes, LCD codes and lattices. Recently, several families of self-orthogonal codes containing the all- vector were constructed by augmentation technique. In this paper, utilizing plateaued functions, we construct some classes of linear codes which do not contain the all- vector. We also investigate their punctured codes. The weight distributions of the constructed codes are explicitly determined. Under certain conditions, these codes are proved to be self-orthogonal. Furthermore, some classes of optimal linear codes are obtained from their duals. Using the self-orthogonal punctured codes, we also construct several new families of at least almost optimal quantum codes and optimal LCD codes.
Cite
@article{arxiv.2502.11599,
title = {Self-orthogonal codes from plateaued functions and their applications in quantum codes and LCD codes},
author = {Yadi Wei and Jiaxin Wang and Fang-Wei Fu},
journal= {arXiv preprint arXiv:2502.11599},
year = {2025}
}