Abstract
The purpose of this manuscript is two-fold. First, properties of the ring \(\mathcal {R}_{k} = \mathbb Z_{2^{k}} + u\mathbb Z_{2^{k}}\) and the set of ideals are established. Second, results on cyclic codes of length n, \(\gcd (2,n)=1\), over the non-chain Frobenius ring \(\mathcal {R}_{k}\) and their description by means of idempotent elements are presented.
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The first author was partially supported by Sistema Nacional de Investigadores, SNI, México and the second author by Fellowship No. 764803, Consejo Nacional de Ciencia y Tecnología, CONACYT, México.
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Communicated by Sergio R. López-Permouth.
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Tapia-Recillas, H., Velazco-Velazco, J.A. Cyclic codes over the ring \(\mathbb {Z}_{2^{k}} + u\mathbb {Z}_{2^{k}}\). São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00412-z
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DOI: https://doi.org/10.1007/s40863-024-00412-z