On the minimum weight of simple full-length array LDPC codes
On the minimum weight of simple full-length array LDPC codes
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DOI：
10.1093/ietfec/e91-a.6.1502
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
K. Sugiyama;Y. Kaji
中科院分区：
文献类型：
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作者：
K. Sugiyama;Y. Kaji
简单全长度阵列LDPC码（Simple and Full Length Array LDPC Codes，简称SFA-LDPC码）是由一类阵列码代数构造而成的LDPC码。SFA-LDPC码的最小码重已有文献研究，但除一些小参数外，尚不清楚其确切的最小码重。本文证明了当p为大于7的素数时，本文中用CA（p，4）表示的SFA-LDPC码类中含有最小权为10或更小的码字.结合CA（p，4）的最小权的杨氏下界，这意味着CA（p，4）的最小权对于任何p > 7的素数p恰好是10。
Simple and full-length array LDPC codes (SFA-LDPC codes) is a class of LDPC codes which are algebraically constructed from a family of array codes. The minimum weight of SFA-LDPC codes has been investigated in literatures, but exact minimum weight of the code is not known except for some small parameters. In this paper it is shown that the class of SFA-LDPC codes which are denoted by CA (p, 4) in this paper contains a codeword whose minimum weight is 10 or less, if p is a prime number greater than 7. Combined with the Yang's lower bound on the minimum weight of CA (p,4), this implies that the minimum weight of CA (p, 4) is exactly 10 for any prime p with p > 7.