On quantum and LCD codes from the cyclic codes over the ring Fq[u,v,w]/⟨u3-u,v2-v,w2-w,uv,vu,uw,wu,vw-wv⟩

Abstract

For an odd prime p and a positive integer r, let q=pr. The objective of this article is to study cyclic codes over the ring S=Fq[u,v,w]/⟨u3-u,v2-v,w2-w,uv,vu,uw,wu,vw-wv⟩ and to construct new and better quantum and LCD codes from them. We give the structure of cyclic codes over the ring S and obtain dual-containing codes over Fq as the Gray images of dual-containing cyclic codes over S. Using these dual-containing codes, we obtain quantum codes and determine their parameters using the decomposition of cyclic codes over the ring S. We provide many new and better-than-existing quantum codes. We also give a method to obtain linear complementary dual (LCD) codes over S using the decomposition of cyclic codes over the ring S. We obtain some optimal and best-known linear codes as Gray images of LCD codes over S. © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024.