Abstract
In this paper, we study cyclic codes and their duals over the local Frobenius non-chain ring \(R={\mathbb {F}}_2[u,v] / \langle u^2=v^2,uv \rangle \), and we obtain optimal binary linear codes with respect to the homogeneous weight over R via a Gray map. Moreover, we characterize DNA codes as images of cyclic codes over R.
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Bulut Yılgör, M., Gürsoy, F., Öztaş, E.S. et al. Cyclic codes over \({\mathbb {F}}_2 +u{\mathbb {F}}_2+v{\mathbb {F}}_2 +v^2 {\mathbb {F}}_2 \) with respect to the homogeneous weight and their applications to DNA codes. AAECC 32, 621–636 (2021). https://doi.org/10.1007/s00200-020-00416-0
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DOI: https://doi.org/10.1007/s00200-020-00416-0