A family of constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2 |
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| Authors: | Xiaoshan Kai Shixin Zhu Liqi Wang |
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| Affiliation: | 1. School of Mathematics, Hefei University of Technology, Hefei, 230009, China
2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China
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| Abstract: | This paper studies (1 + u)-constacyclic codes over the ring F 2 + uF 2 + vF 2 + uvF 2. It is proved that the image of a (1+u)-constacyclic code of length n over F 2+uF 2+vF 2+uvF 2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined. Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2. |
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