Some classes of linear codes over \mathbb {Z}_4+v\mathbb {Z}_4andtheirapplicationstoconstructgoodandnewand their applications to construct good and newandtheirapplicationstoconstructgoodandnew\mathbb {Z}_4$$ -linear codes (original) (raw)

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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Authors and Affiliations

1. School of Science, Shandong University of Technology, Zibo, 255091, People’s Republic of China
   Jian Gao
2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China
   Fang-Wei Fu & Yun Gao

Authors

1. Jian Gao
2. Fang-Wei Fu
3. Yun Gao

Corresponding author

Correspondence toJian Gao.

Additional information

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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• Received: 26 February 2016
• Revised: 12 August 2016
• Accepted: 13 August 2016
• Published: 20 August 2016
• Issue date: March 2017
• DOI: https://doi.org/10.1007/s00200-016-0300-0

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