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On Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$
Published 27 Feb 2014 in cs.IT and math.IT | (1402.6771v2)
Abstract: Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of Euclidean isodual codes, unimodular complex lattices, MDS codes and MGDS codes over $\mathbb{Z}_4+v\mathbb{Z}_4$ are studied. Cyclic codes and quadratic residue codes are also considered. Finally, some examples for illustrating the main work are given.
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