Abstract

By the discussion of division in \(F_{^{^{^{_2 m} } } } \left[ u \right]/\left\langle {u^4 } \right\rangle \), the minimal spanning set and the rank of a (1 + u + u 2) - constacyclic code with an arbitrary length N = 2 e n over \(\Phi \) are determined based on the factorization of (x n - 1) over \({F_{{2^m}}}\).

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