l-LCP of codes and their applications to EAQEC codes

In this paper, we first generalize the complementary pair of codes over finite fields to an l-linear complementary pair (l-LCP) of codes. Then two criteria of l-LCP of codes over finite fields are obtained. We especially investigate l-LCP of constacyclic codes. When C and D are all λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-constacyclic codes, we obtain a characterization of (C, D) to be l-LCP of codes. When C and D are cyclic and negacyclic codes, we give a sufficient condition of (C, D) to be l-LCP of codes. As an application, by means of the l-LCP of codes over finite fields, we exhibit two methods of constructing entanglement-assisted quantum error correcting (EAQEC) codes. Notably, the parameters of our EAQEC codes are new and flexible.