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

Zero-divisor codes are codes constructed using group rings where their generators are zero-divisors. Generally, zero-divisor codes can be equivalent despite their associated groups are non-isomorphic, leading to the proposed conjecture “Every dihedral zero-divisor code has an equivalent form of cyclic zero-divisor code”. This paper is devoted to study equivalence of zero-divisor codes in    $$F_2G$$  F 2 G having generators from the 2-nilradical of    $$F_2G$$  F 2 G , consisting of all nilpotents of nilpotency degree 2 of    $$F_2G$$  F 2 G . Essentially, algebraic structures of 2-nilradicals are first studied in general for both commutative and non-commutative    $$F_2G$$  F 2 G before specialized into the case when  G  is cyclic and dihedral. Then, results are used to study the conjecture above in the cases where the codes generators are from their respective 2-nilradicals.

On equivalence of cyclic and dihedral zero-divisor codes having nilpotents of nilpotency degree two as generators