Simplex codes over the ring $Sigma_{n=0}^s{u^nF_2}$

In this paper, we introduce simplex linear codes over the ring $Sigma_{n=0}^s{u^nF_2}$ of types $alpha$ and $beta$, where $u^{s+1}$=0. And we determine their properties. These codes are an extension and generalization of simplex codes over the ring $Z_{2^s}$.

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