Algorithm 1 Computation of Krawtchouk polynomials using the proposed algorithm.
Input: $N,p$
N represents the size of the Krawtchouk polynomial,
p represents the parameter of the Krawtchouk polynomials.
Output: ${\mathcal{K}}_n^p\left(x\right)$
1: $Flag$=False
2: if $p>0.5$ then
3:     $Flag$=True;       $p\leftarrow p-1$
4: end if
5: $x_0\leftarrow Np$,       $x_1\leftarrow x_0+1$
6: Compute ${\mathcal{K}}_0^p\left(x_0\right)$ using (10)
7: Compute ${\mathcal{K}}_0^p\left(x_1\right)$ using (12)
8: Compute ${\mathcal{K}}_1^p\left(x_0\right)$ and ${\mathcal{K}}_1^p\left(x_1\right)$ using (16) and (17)
9:	▹ Compute initial set
10: for $x=x_0:x_1$ do
11:     for $n=2:x$ do
12:         Compute ${\mathcal{K}}_n^p\left(x\right)$ using (18)
13:     end for
14: end for
15:	▹ Compute coefficient values in Part 1
16: for $n=0:x_0$ do
17:     for $x=x_0:-1:n$do▹ inner loop
18:         Compute ${\mathcal{K}}_n^p\left(x\right)$ using (19)
19:         if $|{\mathcal{K}}_n\left(x\right)|<{10}^{-5}\mathrm{and}\left|{\mathcal{K}}_n(x+1)\right|<{10}^{-7}$ then
20:            Exit inner loop
21:         end if
22:     end for
23: end for
24:	▹ Compute coefficient values in Part 2-1
25: for $n=0:x_0$ do
26:     for $x=x_0:N-n-1$do	▹ inner loop
27:         Compute ${\mathcal{K}}_n^p\left(x\right)$ using (21)
28:         if $|{\mathcal{K}}_n(x+1)|<{10}^{-7}\mathrm{and}\left|{\mathcal{K}}_n\left(x\right)\right|<{10}^{-5}$ then
29:            Exit inner loop
30:         end if
31:     end for
32: end for
33:	▹ Compute coefficient values in Part 2-2
34: for $x=x_0:N/2-1$ do
35:     $n\leftarrow x$
36:     Compute ${\mathcal{K}}_n^p\left(x\right)$ using (23)
37: end for
38: for $x=x_1:N/2-1$ do
39:     $n\leftarrow x$
40:     Compute ${\mathcal{K}}_n^p\left(x\right)$ using (26)
41: end for
42:	▹ Compute coefficient values in Part 2-3
43: for $n=x_1:N/2-2$ do
44:     for $x=n+2:N-n-1$do	▹ inner loop
45:         Compute ${\mathcal{K}}_n^p\left(x\right)$ using (21)
46:         if $|{\mathcal{K}}_n\left(x\right)|<{10}^{-5}\mathrm{and}\left|{\mathcal{K}}_n(x+1)\right|<{10}^{-7}$ then
47:            Exit inner loop
48:         end if
49:     end for
50: end for
51: Compute the rest of the coefficients using the similarity relations (28) and (29)
52: if $Flag$=True then
53:     Apply (30)
54: end if