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On the support weight distribution of linear codes over the ring \(\mathbb{F}_p+u\mathbb{F}_p+\cdots+u^{d-1}\mathbb{F}_p\). (English) Zbl 1369.94601

Summary: Let \(R=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^{2}\mathbb{F}_{p}+\cdots +u^{d-1}\mathbb{F}_{p}\), where \(u^{d}=u\) and \(p\) is a prime with \(d-1\) dividing \(p-1\). A relation between the support weight distribution of a linear code \(\mathcal{C}\) of type \(p^{dk}\) over \(R\) and the dual code \(\mathcal{C}^{\bot}\) is established.

MSC:

94B05 Linear codes (general theory)
94B15 Cyclic codes
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References:

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