Abstract
In this paper, we consider MacDonald codes over the finite non-chain ring \({\mathbb {F}}_p+v{\mathbb {F}}_p+v^2{\mathbb {F}}_p\) and their applications in constructing secret sharing schemes and association schemes, where p is an odd prime and \(v^3=v\). We give some structural properties of MacDonald codes first. Then, we study the weight enumerators of torsion codes of these MacDonald codes. As some applications, constructing secret sharing schemes and association schemes is also investigated.
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Acknowledgements
This research is supported by the National Natural Science Foundation of China (Grant Nos. 11701336, 11626144 and 11671235), and the Scientific Research Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (No. 2018MMAEZD04).
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Communicated by Thomas Aaron Gulliver.
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Wang, Y., Gao, J. MacDonald codes over the ring \({\mathbb {F}}_{p}+v{\mathbb {F}}_{p}+v^2{\mathbb {F}}_{p}\). Comp. Appl. Math. 38, 169 (2019). https://doi.org/10.1007/s40314-019-0937-y
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DOI: https://doi.org/10.1007/s40314-019-0937-y