A new construction of quadratic double circulant LCD codes

Abstract

Let $GF(l)$ be the Galois field with $l=p^m$ elements where $p$ is a prime number and integer $m\geq 1$. Here, we present three constructions for linear codes over $GF(l)$ (depending on the parity of $l$) by using the quadratic residue approach and obtain some sufficient conditions for these codes to be LCD with respect to the Euclidean and Hermitian inner products, respectively. Furthermore, several examples of codes, including optimal and near to optimal codes, are provided to support our study.