CRC-5 correct computation?

Question

I need to generate a CRC table for the standard CRC-5 algorithm, (or at least need some way to validate that the table I have is indeed correct). I was under the impression that CRC-5 would simply utilize 5 bits to calculate the CRC value, but in my table below I notice some first bytes with values greater than 7.

Is this correct and is there a link to a correct CRC5 implementation?

Below is the code I am currently using:

private byte[] _table = new byte[256]
{
    0x00, 0x31, 0x62, 0x53, 0xC4, 0xF5, 0xA6, 0x97,
    0xB9, 0x88, 0xDB, 0xEA, 0x7D, 0x4C, 0x1F, 0x2E,
    0x43, 0x72, 0x21, 0x10, 0x87, 0xB6, 0xE5, 0xD4,
    0xFA, 0xCB, 0x98, 0xA9, 0x3E, 0x0F, 0x5C, 0x6D,
    0x86, 0xB7, 0xE4, 0xD5, 0x42, 0x73, 0x20, 0x11,
    0x3F, 0x0E, 0x5D, 0x6C, 0xFB, 0xCA, 0x99, 0xA8,
    0xC5, 0xF4, 0xA7, 0x96, 0x01, 0x30, 0x63, 0x52,
    0x7C, 0x4D, 0x1E, 0x2F, 0xB8, 0x89, 0xDA, 0xEB,
    0x3D, 0x0C, 0x5F, 0x6E, 0xF9, 0xC8, 0x9B, 0xAA,
    0x84, 0xB5, 0xE6, 0xD7, 0x40, 0x71, 0x22, 0x13,
    0x7E, 0x4F, 0x1C, 0x2D, 0xBA, 0x8B, 0xD8, 0xE9,
    0xC7, 0xF6, 0xA5, 0x94, 0x03, 0x32, 0x61, 0x50,
    0xBB, 0x8A, 0xD9, 0xE8, 0x7F, 0x4E, 0x1D, 0x2C,
    0x02, 0x33, 0x60, 0x51, 0xC6, 0xF7, 0xA4, 0x95,
    0xF8, 0xC9, 0x9A, 0xAB, 0x3C, 0x0D, 0x5E, 0x6F,
    0x41, 0x70, 0x23, 0x12, 0x85, 0xB4, 0xE7, 0xD6,
    0x7A, 0x4B, 0x18, 0x29, 0xBE, 0x8F, 0xDC, 0xED,
    0xC3, 0xF2, 0xA1, 0x90, 0x07, 0x36, 0x65, 0x54,
    0x39, 0x08, 0x5B, 0x6A, 0xFD, 0xCC, 0x9F, 0xAE,
    0x80, 0xB1, 0xE2, 0xD3, 0x44, 0x75, 0x26, 0x17,
    0xFC, 0xCD, 0x9E, 0xAF, 0x38, 0x09, 0x5A, 0x6B,
    0x45, 0x74, 0x27, 0x16, 0x81, 0xB0, 0xE3, 0xD2,
    0xBF, 0x8E, 0xDD, 0xEC, 0x7B, 0x4A, 0x19, 0x28,
    0x06, 0x37, 0x64, 0x55, 0xC2, 0xF3, 0xA0, 0x91,
    0x47, 0x76, 0x25, 0x14, 0x83, 0xB2, 0xE1, 0xD0,
    0xFE, 0xCF, 0x9C, 0xAD, 0x3A, 0x0B, 0x58, 0x69,
    0x04, 0x35, 0x66, 0x57, 0xC0, 0xF1, 0xA2, 0x93,
    0xBD, 0x8C, 0xDF, 0xEE, 0x79, 0x48, 0x1B, 0x2A,
    0xC1, 0xF0, 0xA3, 0x92, 0x05, 0x34, 0x67, 0x56,
    0x78, 0x49, 0x1A, 0x2B, 0xBC, 0x8D, 0xDE, 0xEF,
    0x82, 0xB3, 0xE0, 0xD1, 0x46, 0x77, 0x24, 0x15,
    0x3B, 0x0A, 0x59, 0x68, 0xFF, 0xCE, 0x9D, 0xAC
};

public static byte CalculateCrc(byte[] data, byte startIndex, int count)
{
    byte result = 0;
    for (int i = 0; i < data.Length; i++)
        result = _table[(result ^ data[ii]) & 0xFF];

    return result;
}

Answer 1

Wikipedia says there are three different standard CRC5 polynomials. Which are you using?

I have never worked with CRC5, but I do have some code for CRC32 (IEEE 802.3 Poly) that may help you with your algorithm.

static void GenerateCRCTable(void)
{
    // This is the official polynomial used by CRC32 in PKZip.
    // Often times the polynomial shown reversed as 0x04C11DB7.
    unsigned long dwPolynomial = 0xEDB88320;
    int i      = 0; 
    int j      = 0; 

    unsigned long dwCrc;
    for(i = 0; i < 256; i++)
    {
     dwCrc = i;
     for(j = 8; j > 0; j--)
     {
      if(dwCrc & 1)
       dwCrc = (dwCrc >> 1) ^ dwPolynomial;
      else
       dwCrc >>= 1;
     }

     g_crcTable[i] = dwCrc;
    }
}

Then, in the actual CRC function (some file reading code omitted):

    static bool once     = false;
    wchar_t *t_pfilename = 0;
    int nLen    = 0;

    if(once==false)
    {
        once = true;
        GenerateCRCTable();
    }

    *crc = 0xFFFFFFFF;

    DWORD numRead;
    DWORD i;
    unsigned long value = *crc;

    for(;;)
    {
        if((ReadFile(hCRCFile, g_crcBlock, sizeof(g_crcBlock), &numRead, 0)) == 0)
        {
            CloseHandle(hCRCFile);
            *crc = 0xFFFFFFFF;
            return 2;
        }

        if(numRead == 0)
        {
     break;
        }

     for(i=0; i<numRead; i++)
        {
            value = ((value) >> 8) ^ g_crcTable[(g_crcBlock[i]) ^ ((value) & 0x000000FF)];
        }   
    }

    *crc = ~value;

Answer 2

The bytes in your table have nothing to do with the CRC size. A 32-bit CRC algorithm also (usually, virtually always) use a table of size 256. This has to do with a byte having 256 possible values, and nothing with the CRC.