On Extremal Polynomials Used in Bounds of Code Volume

Delsarte [Philips Res. Rep., 1972, vol. 27, pp. 272–289] found a method of obtaining upper bounds for the volume of a code with specified code distance. The bound obtained via this method is defined by polynomial $H(x)$ that possesses certain particular properties. In this paper it is shown that the polynomials given in [V. I. Levenshtein, Proc. 7th All-Union Conf. on Coding Theory and Information Transmission, vol. 2, Moscow–Vilnius, 1978, pp. 103–108] are extremal for Delsarte's method.