Is the eth residue of p . since the number of quadratic residue mod p is , we can guess the number of eth residue mod p is 2 ^ , and then prove this property . on the basis of eth residue , we construct a type of eth residue code of length p which is an odd prime , and extend some properties of quadratic residue codes . alsi ) we construct a cubic residue code over f % of length 31 and a 4th residue code over fs of length 13 . according to the properties of the bounds of bch codes , we determine the minimal distance of [ 31 , 21 ] code is 5 , which means this code ; can correct two errors 由模p的二次剩余個數(shù)為個,可猜測模p的e次剩余的個數(shù)為個,本文給出了該性質(zhì)的證明。在e次剩余的基礎(chǔ)上,本文構(gòu)造了一類字長p為奇素數(shù)的e次剩余碼,討論了它的性質(zhì),從而推廣了二次剩余碼的一些結(jié)果。利用所導(dǎo)出的理論結(jié)果,我們構(gòu)造了長為31的二元三次剩余碼和長為13的三元四次剩余碼,利用bch碼上下界的性質(zhì),進(jìn)一步確定了31 , 21碼的極小距離為5 ,它可以糾正兩個錯誤。