Trace description and Hamming weights of irreducible constacyclic codes

Irreducible constacyclic codes constitute an important family of error-correcting codesand have applications in space communications.In this paper, we provide a trace description of irreducible constacyclic codes of length \begin{document}$n$\end{document} over the finite field \begin{document}$\mathbb{F}_{q}$\end{document} of order \begin{document}$q,$\end{document} where \begin{document}$n$\end{document} is a positive integer and \begin{document}$q$\end{document} is a prime power coprime to \begin{document}$n.$\end{document} As an application, we determine Hamming weight distributions of some irreducible constacyclic codes of length \begin{document}$n$\end{document} over \begin{document}$\mathbb{F}_{q}.$\end{document} We also derive a weight-divisibility theorem for irreducible constacyclic codes, and obtain both lower and upper bounds on the non-zero Hamming weights in irreducible constacyclic codes. Besides illustrating our results with examples, we list some optimal irreducible constacyclic codes that attain the distance bounds given in Grassl's Table [ 8 ].