Narrow-Sense BCH Codes Over GF(q) With Length n = q(m)-1/q-1
Narrow-Sense BCH Codes Over GF(q) With Length n = q(m)-1/q-1
复制标题
GF(q) 上长度 n = q(m)-1/q-1 的狭义 BCH 代码
DOI：
10.1109/tit.2017.2743687
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发表时间：
2017
影响因子：
2.5
通讯作者：
Ge Gennian
中科院分区：
文献类型：
--
作者：
Li Shuxing;Ding Cunsheng;Xiong Maosheng;Ge Gennian
Cyclic codes are widely employed in communication systems, storage devices, and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most cases among the best cyclic codes. A subclass of good BCH codes are the narrow-sense BCH codes over GF(q) with length n = (qm-1)/(q -1). Little is known about this class of BCH codes when q > 2. The objective of this paper is to study some of the codes within this class. In particular, the dimension, the minimum distance, and the weight distribution of some ternary BCH codes with length n = (3m- 1)/2 are determined in this paper. A class of ternary BCH codes meeting the Griesmer bound is identified. An application of some of the BCH codes in secret sharing is also investigated.
