Abstract
In this paper, we give the complete weight enumerators of two classes of linear codes over the finite field Fp$\mathbb {F}_{p}$, where p is a prime. These linear codes are the torsion codes of MacDonald codes over the finite non-chain ring Fp+vFp$\mathbb {F}_{p}+v\mathbb {F}_{p}$, where v2 = v. We also employ these linear codes to construct systematic authentication codes with new parameters.
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