A Note on Reed-Solomon Codes over Finite Fields
Jun Li · Journal of Sichuan Normal University · 2010
Let Fq be the q elements finite field with characteristic p.Fix a subset D={x1,…,xn}■Fq,which is called the evaluation set.It's well-known that the dual code of the standard Reed-Solomon code Cq(Fq,k) is Cq(Fq,q-k) which is also a Reed-Solomon code.In the present paper,we get a necessary and sufficient condition for that there exists a generalized Reed-Solomon code Cq(B,n-k) such that Cq(D,k) and Cq(B,n-k) are dual to each other.Furthermore,we construct a class of generalized Reed-Solomon codes with the above property.