On LCD Negacyclic Codes over Finite Fields

This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacyclic codes of lengths n=qℓ+12,qm−12(q−1)andqt⋅2τ−12(qt+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = \frac{{{q^\ell } + 1}}{2},\frac{{{q^m} - 1}}{{2\left( {q - 1} \right)}}and\frac{{{q^{t \cdot {2^\tau }}} - 1}}{{2\left( {{q^t} + 1} \right)}}$$\end{document}, respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n|q−12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n|\frac{{q - 1}}{2}$$\end{document} and n|q+12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n|\frac{{q + 1}}{2}$$\end{document}, respectively.