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 study the Hermitian hulls of (extended) generalizedReed-Solomon (GRS and EGRS) codes over finite fields. For a given class of(extended) GRS codes, by increasing the length, increasing the dimensions andincreasing both the length and the dimensions, we obtain three new classes of(extended) GRS codes with Hermitian hulls of arbitrary dimensions. Furthermore,we obtain several new classes of $q^2$-ary maximum distance separable (MDS)codes with Hermitian hulls of arbitrary dimensions. And the dimension of theseMDS codes can be taken from $1$ to $\frac{n}{2}$. By propagation rules, theparameters of the obtained code can be more flexible. As an application, a lotof new (MDS) entanglement-assisted quantum error correction codes (EAQECCs) canbe constructed from previous known (extended) GRS codes. We derive three newpropagation rules on (MDS) EAQECCs constructed from (extended) GRS codes.Finally, we present several new classes of (MDS) EAQECCs with flexibleparameters. Notably, the distance parameters of our codes can range from $2$ to$\frac{n+2}{2}$.

Three classes of propagation rules for GRS and EGRS codes and their applications to EAQECCs