关键词: DNA计算, 海明距离, 线性码, 监督矩阵

Abstract: The encoding problem is a most fundamental issue in DNA computing，the minimal Hamming distance is an important evaluation criterion for measuring coding performance for DNA computation.It is effective method used to construct minimal Hamming distance with linear codes，its key is forming a relevant check matrix for codewords.It presents a search algorithm，optimized means and 2 interrelated necessity theorems for check matrix;It also advances judgment of existence between upper limit and lower limit for minimal Hamming distance，and 2 existence theorems of linear codes;Finally，it gives result of search algorithm for checking matrix over three-alphabet in DNA-based computing，and part of existence result that approach upper limit of codeword amount on GF（3） for DNA computation coding when minimal Hamming distance is definite.In accordance to these results and
existence theorems，it can deduce existence for minimal Hamming distance of typical DNA computation coding without computation on algorithm.

Key words: DNA computation, Hamming distance, linear codes, check matrix