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本文提出了一种建立在组合理论基础上的新编码方法。利用文中所定义的s(u,v)阵列,(n,k,d)线性码的参数可以按k=C(s,v),n-k=C(s,u)及d=min(d_1+l)来确定。令人感兴趣的是很多人们所熟知的一些最佳码字,例如戈莱码、汉明码系列及其扩展码,一类BCH码和复数旋转码等,均可以很方便地由s(u,v)来生成,不需涉及有限域的概念。这种组合方法可以使在已知的最佳码间建立起普遍的关系,并有助于编制搜索程序去发现尚未为人们所知道的其他最佳码字。
This paper presents a new coding method based on combinatorial theory. Using the s (u, v) array defined in the paper, the parameters of the (n, k, d) linear code can be expressed in terms of k = C (s, v), nk = C l) to determine. Interestingly, many of the best codewords well known to many, such as Golay code, Hamming code series and their spreading codes, a class of BCH codes and complex rotation codes, can easily be represented by s (u, v) to generate, without involving the concept of finite fields. This combinatorial approach can establish a universal relationship between the best known codes and help in the development of search programs to discover other best codewords that are not yet known.