The Weight Distribution Of A Class Of Cyclic Codes With Three Nonzeros

Cyclic codes are a subclass of linear codes,and they have been extensively studied since cyclic codes have preferable algebraic properties and efficient decoding algorith-m.cyclic codes have been used to inspect and correct error occurring in transmission of information,and this is an important method to improve the quality of information transmission.therefore it is of theoretical significance and application value to studying cyclic codes.The weight distribution of cyclic codes means the distribution of the Hamming weight of the cyclic codes.The weight distribution of cyclic codes can directly reflect the error correcting capability of cyclic codes,So the weight distribution of cyclic codes is an important topic of error-correcting codes,Especially in recent years the weight distribution of cyclic codes have enjoy much attention.This paper construct a class of cyclic codes over finite with three nonzero ?-1,?-pk+1/2,?-pm-1/2 where p be an odd prime,k and m be positive integers and ? be a primitive element in a finite field Fpm.The weight distribution of the cyclic codes have been determined by using the theory of quadratic forms and particular technique choosing non-square together with other known result.