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\(( 1+\lambda uvw)\)-constacyclic codes over the ring \(\mathbb F_q[u,v,w]/ \langle u^2, v^2, w^2, uv-vu, vw-wv, uw-Wu \rangle\). (English) Zbl 1409.94933

Summary: In this paper, we find constacyclic codes over the ring \[R_{u^2, v^2, w^2, q}= \mathbb{F}_q[u,v,w]/\langle u^2,\ v^2, w^2,\ uv-vu, vw-wv, uw-wu \rangle\] of length \(q-1\) where \(q\) is a power of prime number. We find minimal spanning set and a unique set of generators for these codes. We also show that the Gray image of \((1+\lambda uvw)\)-constacyclic codes of length \(N\) over \(R_{u^2, v^2, w^2, q}\) is a 8-quasicyclic binary linear code of length \(8N\) over \(\mathbb{F}_q\).

MSC:

94B15 Cyclic codes
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