The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.
A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that the algebraic degrees of the new semi-bent functions attain the maximum values.
