Year: 2026
Type: article
Abstract: over the finite local non-Frobenius ring Rp,u,v=Fq+uFq+vFq, u2=v2=uv=vu=0. We define an Fq-linear Gray map πn:Rp,u,vn→Fq6n and investigate the structural properties of Gray images of cyclic codes under this map. It is shown that πn preserves self-orthogonality and, when gcd(n,p)=1, transforms any cyclic code over Rp,u,v into a quasi-cyclic code over Fq of length 6n with index dividing 6. Moreover, we completely characterize the possible quasi-cyclic indices of the Gray images, proving that only the values l∈{1,3,6} can occur, and we establish necessary and sufficient conditions for each case in terms of the generators of the associated cyclic code. Several explicit examples are provided to illustrate the theoretical results and the resulting quasi-cyclic structures.
Source: Entropy
DOI: 10.3390/e28020250
Authors: Sami H. Saif, Alhanouf Ali Alhomaidhi
Institution: King Saud University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: King Saud University
OpenAlex ID: W7130936444
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