English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 ].

Trace description and Hamming weights of irreducible constacyclic codes