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引用次数: 18
摘要
简单全长阵列LDPC码(Simple and full-length array LDPC code，简称SFA-LDPC码)是一类由阵列码族代数构造而成的LDPC码。已有文献对SFA-LDPC码的最小权值进行了研究，但除了一些小参数外，还不知道码的确切最小权值。本文证明，如果p是大于7的素数，则本文用CA (p, 4)表示的SFA-LDPC码类包含一个最小权值小于等于10的码字。结合CA (p,4)的最小权值的杨氏下界，这意味着对于p > 7的任何素数p, CA (p,4)的最小权值正好是10。
On the minimum weight of simple full-length array LDPC codes
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.
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