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

Practically good error-correcting codes should have good parameters andefficient decoding algorithms. Some algebraically defined good codes such ascyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decodingalgorithms. However, many optimal linear codes do not have an efficientdecoding algorithm except for the general syndrome decoding which requires alot of memory. Therefore, it is a natural question whether which optimal linearcodes have an efficient decoding. We show that two binary optimal $[36,19,8]$linear codes and two binary optimal $[40,22,8]$ codes have an efficientdecoding algorithm. There was no known efficient decoding algorithm for thebinary optimal $[36,19,8]$ and $[40,22,8]$ codes. We project them onto the muchshorter length linear $[9,5,4]$ and $[10, 6, 4]$ codes over $GF(4)$,respectively. This decoding algorithms, called {\em projection decoding}, cancorrect errors of weight up to 3. These $[36,19,8]$ and $[40,22,8]$ codesrespectively have more codewords than any optimal self-dual $[36, 18, 8]$ and$[40,20,8]$ codes for given length and minimum weight, implying that thesecodes more practical.

Projection decoding of some binary optimal linear codes of lengths 36 and 40