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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we present a construction of linear codes over $\f_{2^t}$ fromBoolean functions, which is a generalization of Ding's method \cite[Theorem9]{Ding15}. Based on this construction, we give two classes of linear codes$\tilde{\C}_{f}$ and $\C_f$ (see Theorem \ref{thm-maincode1} and Theorem\ref{thm-maincodenew}) over $\f_{2^t}$ from a Boolean function$f:\f_{q}\rightarrow \f_2$, where $q=2^n$ and $\f_{2^t}$ is some subfield of$\f_{q}$. The complete weight enumerator of $\tilde{\C}_{f}$ can be easilydetermined from the Walsh spectrum of $f$, while the weight distribution of thecode $\C_f$ can also be easily settled. Particularly, the number of nonzeroweights of $\tilde{\C}_{f}$ and $\C_f$ is the same as the number of distinctWalsh values of $f$. As applications of this construction, we show severalseries of linear codes over $\f_{2^t}$ with two or three weights by using bent,semibent, monomial and quadratic Boolean function $f$.

A Construction of Linear Codes over $\f_{2^t}$ from Boolean Functions