Abstract
This paper introduces a Gray map from \(\left( {\mathbb{F}_p + v\mathbb{F}_p } \right)^n\) to \(\mathbb{F}_p^{2n}\), and describes the relationship between codes over \(\mathbb{F}_p + v\mathbb{F}_p\) and their Gray images. The authors prove that every cyclic code of arbitrary length n over \(\mathbb{F}_p + v\mathbb{F}_p\) is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.
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This research is supported by NNSF of China under Grant Nos. 11126174, 60973125, 71071045 and 71001032, Talents youth Fund of Anhui Province Universities under Grant No. 2012SQRL020ZD, Youth Science Research Fund of Anhui University under Grant No. 2009QN026B, and the 211 Project of Anhui University Grant No. KJTD002B
This paper was recommended for publication by Editor Lei HU.
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Shi, M., Yang, S. & Zhu, S. Good p-ary quasic-cyclic codes from cyclic codes over \(\mathbb{F}_p + v\mathbb{F}_p\) . J Syst Sci Complex 25, 375–384 (2012). https://doi.org/10.1007/s11424-012-0076-7
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DOI: https://doi.org/10.1007/s11424-012-0076-7