Abstract
Some classes of linear codes over the ring \(\mathbb {Z}_4+v\mathbb {Z}_4\) with \(v^2=v\) are considered. Construction of Euclidean formally self-dual codes and unimodular complex lattices from self-dual codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) are studied. Structural properties of cyclic codes and quadratic residue codes are also considered. Finally, some good and new \(\mathbb {Z}_4\)-linear codes are constructed from linear codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\).
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This research is supported by the National Key Basic Research Program of China (Grant No. 2013CB834204), and the Doctoral Research Program Foundation of Shandong University of Technology (Grant No. 4041/415059).
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Gao, J., Fu, FW. & Gao, Y. Some classes of linear codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) and their applications to construct good and new \(\mathbb {Z}_4\)-linear codes. AAECC 28, 131–153 (2017). https://doi.org/10.1007/s00200-016-0300-0
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DOI: https://doi.org/10.1007/s00200-016-0300-0
Keywords
- Self-dual codes
- Unimodular complex lattices
- Cyclic codes
- Quadratic residue codes
- Gand new \(\mathbb {Z}_4\)-linear codes