Cyclic codes over non-chain ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $ and their applications to quantum and DNA codes
Shakir Ali,
Amal S. Alali,
Kok Bin Wong
et al.
Abstract:<abstract><p>Let $ s \geq 1 $ be a fixed integer. In this paper, we focus on generating cyclic codes over the ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $, where $ \alpha_i \in \mathbb{F}_q\backslash \{0\} $, $ 1 \leq i \leq s $, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility probl… Show more
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