On the Integer Zeros of Krawtchouk Polynomials of Degree 8

Krawtchouk polynomials plays very important role in many different areas of mathematics such as discrete mathematics, coding theory, association schemes and graph theory. The issue of existence of integer zeros of Krawtchouk polynomials is crucial for the existence of combinatorial structures in the Hamming schemes. In this Paper our goal is to investigate the integer zeros of the modified Krawtchouk polynomials of the 8 th order, 𝑄𝑘 𝑛 𝑦 = 𝑘! 𝑃𝑘 𝑛 𝑛−𝑦 2 , where 𝑘 = 8.