Linear Codes with Two Weights or Three Weights from Two Types of Quadratic forms

Let Fq be a finite field with q=pm elements, where p is an odd prime and m is a positive integer. Here, let D0={(x1,x2)∈Fq2\{(0,0)}:Tr(x1pk1+1+x2pk2+1)=c}, where c∈Fq, Tr is the trace function from Fq to Fp and m/(m, k1) is odd, m/(m, k2) is even. Define a p-ary linear code CD=c(a1,a2):(a1,a2)∈Fq2}, where c(a1,a2)=(Tr(a1x1+a2x2))(x1,x2)∈D. At most three-weight distributions of two classes of linear codes are settled.