Three classes of few-weight self-orthogonal projective codes and their applications for LCD codes
Abstract
Since self-orthogonal codes, few-weight codes and linear complementary dual codes(LCD codes, for short) have nice applications in coding theory and cryptography, they have received continuous attention. In 2024, by introducing the notion of the augment code, Heng et al.[16] constructed several classes of few-weight self-orthogonal codes basing on defining sets, which are introduced by Ding et al.[7] in 2007. In this manuscript, for two classes of defining sets, we consider the corresponding augmented codes, construct three classes of four-weight self-orthogonal projective codes and determine the parameters of their dual codes. And then, we construct three classes of LCD codes. In particular, we prove that there exists a class of these LCD codes whose dual codes are almost optimal LCD codes according to the sphere packing bound.
Related
- A G-Invariant Erdős--Hanani Theorem with Applications to Optical Orthogonal and Constant-Weight Codes
- Surjective Stability of Dickson-Siegel-Eichler-Roy Elementary Orthogonal Group over Projective Modules
- Realizability of Cohomology Classes in Orthogonal Grassmannians
- Nef Hattori classes and products of projective lines
- Absolutely universal projective embeddings of long-root geometries of orthogonal type
BibTeX
@misc{huang2026three,
title = {{Three classes of few-weight self-orthogonal projective codes and their applications for LCD codes}},
author = {Yue Huang and Zhonghao Liang and Chenlu Jia and Yongkang Wan and Qunying Liao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.07181},
eprint = {2607.07181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07181},
}
RIS
TY - UNPB
TI - Three classes of few-weight self-orthogonal projective codes and their applications for LCD codes
AU - Yue Huang
AU - Zhonghao Liang
AU - Chenlu Jia
AU - Yongkang Wan
AU - Qunying Liao
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2607.07181
UR - https://arxiv.org/abs/2607.07181
AB - Since self-orthogonal codes, few-weight codes and linear complementary dual codes(LCD codes, for short) have nice applications in coding theory and cryptography, they have received continuous attention. In 2024, by introducing the notion of the augment code, Heng et al.[16] constructed several classes of few-weight self-orthogonal codes basing on defining sets, which are introduced by Ding et al.[7] in 2007. In this manuscript, for two classes of defining sets, we consider the corresponding augmented codes, construct three classes of four-weight self-orthogonal projective codes and determine the parameters of their dual codes. And then, we construct three classes of LCD codes. In particular, we prove that there exists a class of these LCD codes whose dual codes are almost optimal LCD codes according to the sphere packing bound.
ER -