q-元码的平均Hamming距离和方差

On Average Hamming Distance and Variance for q-ary Codes

通过对q元n长码的平均Hamming距离和方差的研究,通过定义函数d(xi,yi),给出了q元n长码的平均Hamming距离和方差的下界。同时当码字数为2k-1(kN)时,其平均Hamming距离和方差能达到下界。

By using the average Hamming distance and variance,we study q-ary code C with length n and number of codewords M ,by the definitiond(xi,yi) function, and give lower bound of the average Hamming distance and variance for q-ary code C with length n.At the same time,when the numbers of code are 2k-1(kN),its average Hamming distance and variance can reach the lower bound.