/*
  Author:  Pate Williams (c) 1997

  Exercise 10.4
  "Construct an orthogonal array OA(3, 13, 3)."
  -Douglas R. Stinson-
  See "Cryptography: Theory and Practice by
  Douglas R. Stinson page 325.
*/

#include <stdio.h>

long radix_representation(long b, long A, long *a)
{
  long i = 0, q, x = A;

  q = x / b, a[i] = x - q * b;
  while (q > 0)
    i++, x = q, q = x / b, a[i] = x - q * b;
  return i + 1;
}

int main(void)
{
  int found;
  long count = 0, i, j, k, length, p = 3, s;
  long R[27][3], C[27][3];

  printf("R\n");
  for (i = 0; i < 27; i++) {
    length = radix_representation(3, i, R[i]);
    for (j = length; j < 3; j++) R[i][j] = 0;
    for (j = 2; j >= 0; j--)
      printf("%d", R[i][j]);
    printf(" ");
    if ((i + 1) % 8 == 0) printf("\n");
  }
  for (i = 0; i < 27; i++) {
    found = 0;
    for (j = 2; !found && j >= 0; j--) {
      found = R[i][j] != 0;
      if (found) k = j;
    }
    if (found) {
      if (R[i][k] == 1) {
        for (j = 0; j < 3; j++)
          C[count][j] = R[i][j];
        count++;
      }
    }
  }
  printf("\nC\n");
  for (i = 0; i < count; i++) {
    for (j = 2; j >= 0; j--)
      printf("%d", C[i][j]);
    printf(" ");
    if ((i + 1) % 8 == 0) printf("\n");
  }
  printf("\nOA(3, 13, 3)\n");
  for (i = 0; i < 27; i++) {
    for (j = 0; j < count; j++) {
      s = 0;
      for (k = 2; k >= 0; k--)
        s += R[i][k] * C[j][k];
      s %= p;
      printf("%d ", s);
    }
    printf("\n");
  }
  return 0;
}