CRC编码程序中的编译错误

我为执行CRC编码的程序编写了以下代码。我模仿了我们在课堂上教授的C程序。它给出了一些我无法纠正的编译错误。我在代码之后提到了它们。

I wrote the following code for a program that performs CRC encoding. I modeled it on a C program that we were taught in class. It gives some compilation errors that I can't correct. I have mentioned them after the code.
1 #include<iostream>
2 #include<string.h>
3
4 using namespace std;
5
6 class crc
7 {
8   char message[128],polynomial[18],checksum[256];
9   public:
10  void xor()
11  {
12      for(int i=1;i<strlen(polynomial);i++)
13          checksum[i]=((checksum[i]==polynomial[i])?'0':'1');
14  }
15  crc()    //constructor
16  {
17      cout<<"Enter the message:"<<endl;
18      cin>>message;
19      cout<<"Enter the polynomial";
20      cin>polynomial;
21  }
22  void compute()
23  {
24      int e,i;
25      for(e=0;e<strlen(polynomial);e++)
26      checksum[e]=message[e];
27      do
28      {
29          if(checksum[0]=='0')
30          xor();
31          for(i=0;i<(strlen(polynomial)-1);i++)
32              checksum[i]=checksum[i+1];
33          checksum[i]=message[e++];
34      }while(e<=strlen(message)+strlen(checksum)-1);
35  }
36  void gen_proc() //general processing
37  {
38      int mesg_len=strlen(message);
39      for(int i=mesg_len;i<mesg_len+strlen(polynomial)-1;i++)
40          message[i]='0';
41      message[i]=''; //necessary?
42      cout<<"After appending zeroes message is:"<<message;
43      compute();
44      cout<<"Checksum is:"<<checksum;
45      for(int i=mesg_len;i<mesg_len+strlen(polynomial);i++)
46      message[i]=checksum[i-mesg_len];
47      cout<<"Final codeword is:"<<message;
48  }
49 };
50 int main()
51 {
52  crc c1;
53  c1.gen_proc();
54  return 0;
55 }

编译错误为：

crc.cpp:10: error: expected unqualified-id before ‘^’ token
crc.cpp: In member function ‘void crc::compute()’:
crc.cpp:30: error: expected primary-expression before ‘^’ token
crc.cpp:30: error: expected primary-expression before ‘)’ token
crc.cpp: In member function ‘void crc::gen_proc()’:
crc.cpp:41: warning: name lookup of ‘i’ changed for ISO ‘for’ scoping
crc.cpp:39: warning:   using obsolete binding at ‘i’

我一直在网上检查这些错误，我唯一看到的是由不正确的数组处理引起的错误。我已经仔细检查了我的代码，但我似乎没有执行任何不正确的数组访问。