@article{Ma2024, 
author = {Lijun Ma and Shuxia Liu and Zihong Tian},
title = {The binary codes generated from quadrics in projective spaces},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {29333-29345},
keywords = {quadric, conic, binary code, generator matrix, dimension},
url = {https://www.sciopen.com/article/10.3934/math.20241421},
doi = {10.3934/math.20241421},
abstract = {Quadrics are important in finite geometry and can be used to construct binary codes. In this paper, we first define an incidence matrix  M based on points and non-degenerate quadrics in the classical projective space PG (n−1,q), where  q is a prime power. As a consequence, we establish a binary code  C(M) with the generator matrix  M and determine the dimension of  C(M) when  q and  n are both odd. In particular, we study the minimum distances of  C(M) and  C⊥(M) in PG (2,q) and give their upper bounds.}
}