Separable additive quadratic residue codes over $Z_2Z_4$ and their applications

Abstract

This paper examines separable additive quadratic residue codes (QRCs) over $\mathbb{Z}_{2}\mathbb{Z}_{4}$ and their applications. The idempotent generators of these codes are obtained. Further, the properties of separable additive QRCs over $\mathbb{Z}_{2}\mathbb{Z}_{4}$ are studied including their idempotent generators. As applications, these codes are used to construct self-dual, self-orthogonal, additive complementary pair (ACP) codes, additive complementary dual (ACD) codes, and additive $l$-intersection pairs of codes over $\mathbb{Z}_{2}\mathbb{Z}_{4}$.