\((1+\lambda u^2)\)-constacyclic codes of arbitrary length over \(F_{p^m}[u]/\langle u^3\rangle \)
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Abstract
The generators for \((1+\lambda u^2)\)-constacyclic codes of arbitrary length over \(F_{p^m}[u]/\langle u^3\rangle \) are given. As a special case, we get generators for \((1+\lambda u^2)\)-constacyclic codes with length \(p^e\) over \(F_{p^m}[u]/\langle u^3\rangle \). Besides, we determine generators for the dual codes of \((1+\lambda u^2)\)-constacyclic codes with an arbitrary length over \(F_{p^m}[u]/\langle u^3\rangle \). Based on this, the necessary and sufficient condition for being a self-dual \((1+\lambda u^2)\)-constacyclic code over \(F_{2^m}[u]/\langle u^3\rangle \) is derived.
Keywords
Constacyclic code Cyclic code Self-dual code GeneratorReferences
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