#OK to post
#GLORIA LIU, Mar 5 2024, Assignment 14

read `C14.txt`:

#=====================================#
#1. Generalize procedures Encode113(x), RV113(), and Syl113(x), call them
#Enocde113G(x,q), Sy113G(x,q), and Decode113G(y,q)
#that generalizes the code of Ex. 11.3 from n=10 to general n, and from q=11 to general prime q.

#I am going to use my code from the last homework 
with(LinearAlgebra):
Encode113G:=proc(x,q) local n,m,H,H1,K,i,j,t,result:
m:=nops(x):
n:=nops(x) + 4:
H:=[seq([seq(i^j, i=1..n)], j=0..3)]:
#print(H);
H1:=[seq([seq(H[i][j], j=m+1..n)], i=1..4)]:
#print(H1);
K:=[seq(-1*add(H[i][j]*x[j],j=1..m) mod q, i=1..4)]:
t:=Linsolve(Matrix(H1),Vector(K)) mod q:
[op(x), seq(t[i], i=1..4)]:
end:

Sy113G:=proc(x,q) local i,r:
[seq(add(i^(r-1)*x[i],i=1..nops(x)) mod q,r=1..4)]:
end:

Decode113G:=proc(y,q) local S,eq,i,j,L,i1,a,b:
S:=Sy113G(y,q):
if S=[0$4] then
 RETURN(y):
fi:
eq:=(S[2]^2-S[1]*S[3])*i^2+(S[1]*S[4]-S[2]*S[3])*i+(S[3]^2-S[2]*S[4]) mod q:
if eq=0 then
 i:=S[2]/S[1] mod q:
 a:=S[1]:
 RETURN(y-[0$(i-1), a, 0$(nops(y)-i)] mod q):
fi:
L:=[]:
for i1 from 0 to q-1 do
 if subs(i=i1, eq) mod q=0 then
  L:=[op(L), i1]:
 fi:
od:
i:=L[1]:
j:=L[2]:
print(L);
b:=(i*S[1]-S[2])/(i-j) mod q:
a:=S[1]-b mod q:
print([a,b]);
[[i,a],[j,b]]:
print(nops(y));
print([0$(i-1),a,0$(j-i-1),b,0$(nops(y)-j)]);
y-[0$(i-1),a,0$(j-i-1),b,0$(nops(y)-j)] mod q:
end:

#Testing: inputs prime q and m, the length of the message to encode
#That means the codeword will have length m+4
#q>m+4
RV113G:=proc(q,m) local v,x,y,x1,x2:
v:=RV(q,m):
print(v);
x:=Encode113G(v,q):
print(x);
print(Sy113G(x,q));
y:=Decode113G(x,q):
print(y):
x2:=x+[1,0$(m+3)]:
print(Decode113G(x2, q));
x1:=x+[1, 0$(m+2), 1]:
print(Decode113G(x1, q));
end:

RV113G(11, 6);

#=====================================#
#2. Read and understand Chapter 11 of the book and Ramanujan's paper
#Done