关于二元线性分组码的快速译码

On fast decoding of binary linear block codes

Ｐｌｅｓｓ提出了由ＧＦ（４）上的（６，３，４）线性分组码构造二元（２４，１２，８）Ｇｏｌａｙ码的投影方法，并据此给出了二元Ｇｏｌａｙ码的快速译码算法，Ｖａｒｄｙ和Ｂｅ＇ｅｒｙ又利用四元（６，３，４）码的码字与二元（２４，１２，８）Ｇｏｌａｙ码的码字间的投影关系提出了到目前为止最有效的Ｇｏｌｓｙ码的最大似然软判决译码算法．下文进一步推广了Ｐｌｅｓｓ提出的投影方法，给出了由四元（ｎ，ｋ，ｄ）线性分组码构造的二元（４ｎ，ｎ＋２ｋ≥ｍｉｎ（ｎ，２ｄ，８）线性分组码，并以（２８，１５，６）码的译码为例说明这类码的译码过程．

Plass presented a projecting method for constructing a binary (24, 12, 8) Golay code fromthe (6, 3, 4) linear code over GF(4), and so proposed a fact decoding algorithm for the Golaycode. Vardy and Be'ery gave, to the best of our knowledge, the most efficient maximum likelihood decoding algorithm for the code by utilizing the projecting relation between the codewordsof the quaternary (6, 3, 4) code and those of the binary (24, 12, 8) Golay code. Here, we further generalize the projecting method propaned by Pless, and give a binary (4n, n+2k, ≥min(n, 2d, 8)) code from a quaternary (n, k, d ) code. Finally, decoding procedure of the codes isillustrated by that of the binary (28, 15, 6) block code.