Abstract
We construct an infinite family of commutative rings \({R_{q,\varDelta }}\) and we study codes over these rings as well as the structure of the rings. We define a canonical Gray map from \({R_{q,\varDelta }}\) to vectors over the residue finite field of q elements and use it to relate codes over \({R_{q,\varDelta }}\) to codes over the finite field \({\mathbb {F}}_q\). Finally, we determine the parameters for when self-dual codes exist and give various constructions for self-dual codes over \({R_{q,\varDelta }}\).
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Acknowledgements
This work has been partially supported by the Spanish MINECO under Grant PID2019-104664GB-I00 (AEI/FEDER, UE).
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This work has been partially supported by the Spanish MINECO Grants TIN2013-40524-P and MTM2015-69138-REDT, and by the Catalan AGAUR Grant 2014SGR-691.
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Dougherty, S.T., Fernández-Córdoba, C. & Ten-Valls, R. Self-dual codes over a family of local rings. AAECC 32, 265–281 (2021). https://doi.org/10.1007/s00200-020-00466-4
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DOI: https://doi.org/10.1007/s00200-020-00466-4