The addition and multiplication operation based on extended base are given.With the codons set , firstly, Hamming distance is defined.Then H*-distance is obtained by weighting and improving Hamming distance.More cross products among the codons are also defined.Finally, by using above definitions, several types of cancers related to p53 gene are analyzed.By comparison, the following results have been obtained: When, the first base mutates.But when, the second base mutates.When the second mutates, the H*-inner product is less than or equal to 0.By means of the comparison of Hamming distance and H*-distance, the latter is more useful for the study of the properties of amino acids.These results are not only important for further study of the amino acids by encoded codons occurring mutation, but also can be as some guidance for the action of preventing and controlling malignant tumor .