#Homework 6, Isaac Lam, February 13th 2024

#Old class code

# a random word of length n in {0, ..., q-1}
RV:=proc(q,n):
	return [seq(rand(0..q-1)(),1..n)];
end;

# LtoC(q,M): inputs a list of basis vectors for our linear code over GF(q)
# outputs all the codewords (the actual subset of GF(q)^n with q^k elements)
LtoC:=proc(q,M) local n,k,C,i,M1,c:
    option remember;
    
    k:=nops(M);
    n:=nops(M[1]);

    if k=1 then
        return {seq(i*M[1] mod q, i=0..q-1)};
    fi;

    M1:=M[1..k-1];
    C:=LtoC(q, M1);
    return {seq(seq(c + i*M[k] mod q, i=0..q-1), c in C)};
end;

# MinW(q,M): The minimal weight of the linear code generated by M over GF(q)
MinW:=proc(q,M) local n,c,C:
    n:=nops(M[1]);
    C:=LtoC(q,M);

    return min(seq(HD(c, [0$n]), c in C minus {[0$n]}));
end;
#End of class code

#3.
SearchLC:=proc(q,n,k,K): local i,j,currM,currW,M,W:

    W:=0:
    M:=[]:

    for i from 1 to K do:
        currM:=[]:
        for j from 1 to k do:
            currM:=[op(currM), RV(q,n)]:
        end do:

        w:=MinW(q,M):
        if w > W then
            W:=currW:
            M:=currM:
        end if:
    end do:

    M:

end:

#4. skipped