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The Laws of Cryptography with Java Code.

Here is a test of the Hamming mod 11 Error Correcting code, using 3 check digits and 121 digits altogether. The test starts with a random initial word. It first inserts the proper check digits in positions 0, 1 and 11. The test then makes a random change in each position and corrects the change, so there are 121 changes (some are 0 added -- no change). In repeated runs, the code has always corrected the proper position to the old value.

// H11EC.java: Implement the mod 11 Hamming code 
public class H11EC {

   public static int[] inv = {0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};

   // Using the sum1 check sum, if have error e and check1 result c,
   //    then pos[e][c] gives the position in error (modulo 11),
   //    using the first check equation.
   //   If the error is e and check11 result is c,
   //    then pos[e][c] gives the value position/11.
   public static int[][] pos = {
         {0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},  
         {0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10},
         {0,  6,  1,  7,  2,  8,  3,  9,  4, 10,  5},
         {0,  4,  8,  1,  5,  9,  2,  6, 10,  3,  7},
         {0,  3,  6,  9,  1,  4,  7, 10,  2,  5,  8},
         {0,  9,  7,  5,  3,  1, 10,  8,  6,  4,  2},
         {0,  2,  4,  6,  8, 10,  1,  3,  5,  7,  9},
         {0,  8,  5,  2, 10,  7,  4,  1,  9,  6,  3},
         {0,  7,  3, 10,  6,  2,  9,  5,  1,  8,  4},
         {0,  5, 10,  4,  9,  3,  8,  2,  7,  1,  6},
         {0, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1}};

   public static void printArray(int[] a) {
      for (int i = 0; i < a.length; i++) {
      	 if (a[i] == 10)
      	    System.out.print("X ");
      	 else
      	    System.out.print(a[i]);
      	 if (i%5 == 0) System.out.print(" ");
      }
      System.out.println();
   }
   
   public static void printUnchecked(int[] a) {
      System.out.print("? "); // position 0
      System.out.print("?"); // position 1
      for (int i = 2; i < a.length; i++) {
         if (i == 11) System.out.print("?"); // position 11
         else System.out.print(a[i]);
      	 if (i%5 == 0) System.out.print(" ");
      }
      System.out.println();
   }

   public static void insertCheck(int[] a) {
      a[1] = inv[sum1NoCheck(a)];
      a[11] = inv[sum11NoCheck(a)];
      a[0] = inv[sum0NoCheck(a)];
      if (!doCheck(a))
         System.out.println("Failure in insertCheck");
   }
   
   public static boolean doCheck(int[] a) {
      int error = sum0(a); // amount of error
      int check1 = sum1(a);
      int check11 = sum11(a);
      if (error == 0 && check1 == 0 && check11 == 0) return true;
      if (error == 0) return false; // a double error
      int position = pos[error][check11]*11 + pos[error][check1];
      if (position >= a.length) {
      	 System.out.println("doCheck: position: " + position +
      	    ", error: " + error + ", check1: " + check1 +
      	    ", check11: " + check11);
      	 System.exit(0);
      }
      	 
      a[position] = (a[position] - error + 11)%11;
      System.out.println("Position " + position + " corrected to " + 
         a[position]);
      return true;
   }

   public static int sum0(int[] a) {
      int check = 0;
      for (int i = 0; i < a.length; i++)
         check = (check + a[i])%11;
      return check;
   }

   public static int sum0NoCheck(int[] a) {
      int check = 0;
      for (int i = 1; i < a.length; i++)
         check = (check + a[i])%11;
      return check;
   }

   public static int sum1(int[] a) {
      int check = 0;
      for (int i = 0; i < a.length; i++)
         check = (check + (i%11)*a[i])%11;
      return check;
   }

   public static int sum1NoCheck(int[] a) {
      int check = 0;
      for (int i = 2; i < a.length; i++)
         check = (check + (i%11)*a[i])%11;
      return check;
   }
   
   public static int sum11(int[] a) {
      int check = 0;
      for (int i = 0; i < a.length; i++)
         check = (check + ((i/11)%11)*a[i])%11;
      return check;
   }
   
   public static int sum11NoCheck(int[] a) {
      int check = 0;
      for (int i = 12; i < a.length; i++)
         check = (check + ((i/11)%11)*a[i])%11;
      return check;
   }
   
   // main function
   public static void main (String[] args) {
      int[] a = new int[121];
      boolean checkFlag = false;
      for (int i = 0; i < a.length; i++)
         if (i != 11) a[i] = (int)(Math.random() * 10.0);
      for (int i = 0; i < a.length; i++) {
         // H11EC.printUnchecked(a);
         H11EC.insertCheck(a);
         // H11EC.printArray(a);
         // System.out.println(H11EC.doCheck(a));
         int oldValue = a[i];
         a[i] = (a[i] + (int)(Math.random() * 10.0))%10;
         System.out.print("Position: " + i + " changed from " +
             oldValue + " to " + a[i] + "; ");
         if (oldValue == a[i]) System.out.println();
         // H11EC.printArray(a);
         // System.out.println(H11EC.doCheck(a));
         H11EC.doCheck(a);
         if (a[i] != oldValue) System.out.println("**************************");
         // H11EC.printArray(a);
         // System.out.println("******************************");
      }
   } // end of main
} 

% java H11EC
Position: 0 changed from 10 to 3; Position 0 corrected to 10
Position: 1 changed from 10 to 3; Position 1 corrected to 10
Position: 2 changed from 1 to 1; 
Position: 3 changed from 0 to 2; Position 3 corrected to 0
Position: 4 changed from 0 to 0; 

  . . . (many lines omitted) . . .

Position: 117 changed from 4 to 1; Position 117 corrected to 4
Position: 118 changed from 5 to 6; Position 118 corrected to 5
Position: 119 changed from 4 to 9; Position 119 corrected to 4
Position: 120 changed from 7 to 7;