关于q元BCH码的维数和最小距离
ON THE DIMENSION AND MINIMUM DISTANCE OF BCH CODES OVER GF(q)
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摘要: 本文讨论的是q元狭义本原BCH码,以下简称BCH码。首先给出了一定条件下求BCH码维数的一般公式,该结果改进了MacWilliams等人(1977)的结果。然后给出了求BCH码维数的一般迭代方法。此外,本文还指出了BCH码的最小距离的BCH界是分圆陪集首,我们猜测BCH码的最小距离也是分圆陪集首。
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关键词:
- BCH码; 分圆陪集; 维数; 最小距离
Abstract: At first, a formula for computing the dimension of (narrow-sense, primitive) BCH codes over GF(q) is offered, which is better than the result given by F. J. MacWilliams et al. (1977). then a new method for calculating the dimension of BCH codes is proposed. Moreover, it is proved that BCH bound is a leader of cyclotomic cosets, and it is guessed that the minimum distance of BCH codes is also a leader of cvclotomic cosets. -
MacWilliams F J, Sloane N J A. The Theory of Error-Correcting Codes. Amsterdam: North-Holland,[2]Publishing Company. 1977, 201-267.[3]岳殿武.循环陪集结构及其应用.系统科学与数学,1992, 12(1): 15-20.[4]岳殿武,纪青君.关于Goppa码、Alternant码最小距离下限的简化算法.通信学报,1991, 12(3): 10-16.[5]Augot D, Charpin P, Sendrier N. IEEE Trans. on IT, 1992, IT-38(3): 960-973.[6]Cohen G. IEEE Trans. on IT, 1980, IT-26(3): 363.[7]Peterson W W. J. IECE Japan, 1967, 50(6): 1183-1190.[8]Kasami T, Tokura N. IEEE Trans. on IT, 1969, IT-15(3): 408-413.[9]Helleseth T. Discrete Applied Mathematics, 1985, (11): 157-173. -
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