Alternate Encoding Interpretation

The 16-byte (128-bit) ASCII encoding for the 32-bit checksum provides a large degree of redundancy in the precise string that is used to express any given value. A straightforward estimate suggests that there are about 10²⁹ = 2¹²⁸/2³² different ASCII patterns that represent each unsigned 32-bit integer. If only the 62 alpha-numeric characters are allowed in the encoded strings, this number is reduced by a factor of about 10¹⁰ = (62/256)¹⁶ to 10¹⁹ total ASCII expressions for each possible FITS checksum.

This proposal does not mandate a single ASCII encoding algorithm selected from this very large number of possibilities, although the encoding described in §3.4 and §3.5 and in the code in the appendices is recommended. The following constraints on the ASCII encoded values are required, however:

• The 32-bit unsigned integer checksum will be encoded into a 16 character ASCII string.
• Only the ASCII alpha-numeric characters, 0-9, A-Z and a-z, are permitted.
• The quotes enclosing the ASCII string in the CHECKSUM keyword value will lie in columns 11 and 28. The implications of this are discussed in §3.7 below.
• The encoded ASCII value will cause the 32-bit 1's complement checksum of the particular FITS HDU to be zeroed.