Abstract
In this paper, cyclic codes over the ring R = F q + uF q + vF q + uvF q + are discussed where the ring R is not a finite chain ring. By studying the polynomial ring ℜ n = (F q + uF q + vF q + uvF q )[x/(x n − 1) and using the corresponding relationship between the cyclic codes in R and the ideals in ℜ n , cyclic codes over the ring R are characterized. Finally, a Gray-map is obtained and the image of cyclic codes in R is characterized.
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Foundation item: Supported by the Natural Science Foundation of Hubei Province (B20114410)
Biography: XU Xiaofang, female, Master, Lecturer, research direction: algebra combination and algebra coding.
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Xu, X., Liu, X. On the structure of cyclic codes over F q + uF q + vF q + uvF q . Wuhan Univ. J. Nat. Sci. 16, 457–460 (2011). https://doi.org/10.1007/s11859-011-0780-5
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DOI: https://doi.org/10.1007/s11859-011-0780-5