The symmetry group of Z(q)(n) in the Lee space and the Z(qn)-linear codes

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1997-01-01

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Springer

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The Z(4)-linearity is a construction technique of good binary codes. Motivated by this property, we address the problem of extending the Z(4)-linearity to Z(q)n-linearity. In this direction, we consider the n-dimensional Lee space of order q, that is, (Z(q)(n), d(L)), as one of the most interesting spaces for coding applications. We establish the symmetry group of Z(q)(n) for any n and q by determining its isometries. We also show that there is no cyclic subgroup of order q(n) in Gamma(Z(q)(n)) acting transitively in Z(q)(n). Therefore, there exists no Z(q)n-linear code with respect to the cyclic subgroup.

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Applied Algebra, Algebraic Algorithms and Error-correcting Codes. Berlin 33: Springer-verlag Berlin, v. 1255, p. 66-77, 1997.

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