A Class Of Exponential Sum And The Weight Distribution Of A Class Of Cyclic Code

This dissertation studied the value distribution of a class of exponential sum and the weight distribution of a class of cyclic codes,and they can be describing as follows:They defined a cyclic code from trace function,and studied the exponential sum by using half quadratic binomial.Firstly,let Fq is a finite field with elements q=Pr and characteristic p.Let d=pr-1/pe+1-pr-1/2 and e is an integer with pe-1|(pr+1/pe+1-1)this case,they studied the value and the value distribution of S(?,?).That is,they computed the value and its distribution of T(?,?)by using quadratic binomial in Fq,and then determined the value and its distribution of S(?,?)=?(?)for a special index d =pr-1/pe+1-pr-1/2according to T(?,?).Secondly,they constructed several class of few-weight cyclic code by using Gauss sum over finite field,and gave the weight distribution of these codes in different case.Specifically,they constructed few-weight cyclic code in the case of gcd(q-1,l)= 1,gcd(q-1,l)=t,t ?2,l = pe+1,and computed their weight distribution.They also constructed a class of two-weight cyclic code in the case of l = 1 and p = 3,d0 =1,and gave the weight distribution of such code.