2022/06/17 by Astha Agrawal, Agrawal, Astha, Gyanendra K. Verma +3
Computer Science · Social Sciences · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication
paper · pdf · doi:10.48550/arxiv.2206.08725
openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \citeanote, Wu and Shi studied l -Galois LCD codes over finite chain ring R=\mathbbFq+u\mathbbFq, where u2=0 and q=pe for some prime p and positive integer e. In this work, we extend the results to the finite non chain ring R =\mathbbFq+u\mathbbFq+v\mathbbFq+uv\mathbbFq, where u2=u,v2=v and uv=vu . We define a correspondence between l -Galois dual of linear codes over R and l -Galois dual of its component codes over \mathbbFq . Further, we construct Euclidean LCD and l -Galois LCD codes from linear code over R . This consequently leads us to prove that any linear code over R is equivalent to Euclidean ( q>3 ) and l -Galois LCD (0