Abstract
In this paper, we give the complete weight enumerators of two classes of linear codes over the finite field \(\mathbb {F}_{p}\), where p is a prime. These linear codes are the torsion codes of MacDonald codes over the finite non-chain ring \(\mathbb {F}_{p}+v\mathbb {F}_{p}\), where v 2 = v. We also employ these linear codes to construct systematic authentication codes with new parameters.
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Acknowledgments
Part of this work was done when J. Gao was visiting the Chern Institute of Mathematics, Nankai University, Tianjin, China. J. Gao would like to thank the institution for the kind hospitality. This research is supported by the National Key Basic Research Program of China (973 Program Grant No. 2013CB834204), the National Natural Science Foundation of China (Nos. 61571243, 61171082 and 11526045), the Doctoral Research Foundation of Shandong University of Technology (No. 4041/415059) and the Innovation Research Program of Postgraduate Teaching of Shandong University of Technology (No. 4052/115017).
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Wang, X., Gao, J. & Fu, FW. Complete weight enumerators of two classes of linear codes. Cryptogr. Commun. 9, 545–562 (2017). https://doi.org/10.1007/s12095-016-0198-1
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DOI: https://doi.org/10.1007/s12095-016-0198-1