#OK to post homework
#Joseph Koutsoutis, 02-18-2024, Assignment 9

#Note: the version of C9.txt currently on the class page can't be read 
#since antiPCM takes H as both an argument and local variable.
#I just removed this function in my version of the file.
read `C9.txt`:

#1

#Here are the names and ages mod 26:

#AlexVarjabedian - 19
#AuroraHiveley - 23 
#GloriaLiu - 21
#HimanshuChandra - 22
#IssacLam - 18
#JosephKoutsoutis - 20
#KayleeWeatherspoon - 22
#LucyMartinez - 25
#NatalyaTer-Saakov - 24
#PabloBlanco - 21
#RameshBalaji - 19
#RyanBadi - 20
#ShauryaBaranwal - 19

#All of the ciphers looked consistent when I checked.

#2

antiPCM:=proc(q,H) local k,n,i,j,M:
n:=nops(H[1]):
k:=n-nops(H):

if [seq([op(k+1..n,H[i])],i=1..n-k)]<>[seq([0$(i-1),1,0$(n-k-i)],i=1..n-k)] then
 RETURN(FAIL):
fi:

for i from 1 to k do
 for j from 1 to k do
  if i=j then
   M[i,j] := 1:
  else
   M[i,j] := 0:
  fi:
 od:
 for j from k+1 to n do
  M[i,j] := -H[j-k,i] mod q:
 od:
od:
[seq([seq(M[i,j],j=1..n)],i=1..k)]:
end:

#3

DecodeLT := proc(q,M) local v,V,synT,T,S,n,H:
 n := nops(M[1]):
 synT,S := SynT(q, SFde(q, M)):
 H := PCM(q,SFde(q,M)):
 V := Fqn(q,n):
 for v in V do:
  T[v] := v - synT[Syn(q,H,v)] mod q:
 od: 
 op(T):
end: