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

Recent years, several new types of codes were introduced to providefault-tolerance and guarantee system reliability in distributed storagesystems, among which locally repairable codes (LRCs for short) have played animportant role.  A linear code is said to have locality $r$ if each of its code symbols can berepaired by accessing at most $r$ other code symbols. For an LRC with length$n$, dimension $k$ and locality $r$, its minimum distance $d$ was proved tosatisfy the Singleton-like bound $d\leq n-k-\lceil k/r\rceil+2$. Since then,many works have been done for constructing LRCs meeting the Singleton-likebound over small fields.  In this paper, we study quaternary LRCs meeting Singleton-like bound througha parity-check matrix approach. Using tools from finite geometry, we providesome new necessary conditions for LRCs being optimal. From this, we prove thatthere are $27$ different classes of parameters for optimal quaternary LRCs.Moreover, for each class, explicit constructions of corresponding optimalquaternary LRCs are presented.

Optimal Quaternary Locally Repairable Codes Attaining the Singleton-like Bound