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The Fletcher checksum cannot distinguish between blocks of all 0 bits and blocks of all 1 bits. For example, if a 16-bit block in the data word changes from 0x0000 to 0xFFFF, the Fletcher-32 checksum remains the same. This also means a sequence of all 00 bytes has the same checksum as a sequence (of the same size) of all FF bytes.
BSD checksum (Unix) 16 bits sum with circular rotation SYSV checksum (Unix) 16 bits sum with circular rotation sum8 8 bits sum Internet Checksum: 16 bits sum (ones' complement) sum24 24 bits sum sum32 32 bits sum fletcher-4: 4 bits sum fletcher-8: 8 bits sum fletcher-16: 16 bits sum fletcher-32: 32 bits sum Adler-32: 32 bits sum xor8: 8 bits ...
The checksum algorithms most used in practice, such as Fletcher's checksum, Adler-32, and cyclic redundancy checks (CRCs), address these weaknesses by considering not only the value of each word but also its position in the sequence. This feature generally increases the cost of computing the checksum.
The test vectors for Fletcher-16 and Fletcher-32 would be more useful if the endian-ness of the conversion of the ASCII characters to 16- and 32-bit blocks were stated and how the given word (vector) has been padded to a whole number of blocks.
Adler-32 is a checksum algorithm written by Mark Adler in 1995, [1] modifying Fletcher's checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed. Adler-32 is more reliable than Fletcher-16 , and slightly less reliable than Fletcher-32 .
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The data format consists of a header, followed by the compressed data. The header contains an identifier and house keeping information, such as compressed and decompressed data sizes and a 32-bit checksum (a variant of the Fletcher checksum). The compressed data starts with four bytes, identifying four unique 8-bit marker symbols (m1, m2, m3 ...
It's not hard to derive from the specification (you need another "base" of course, I'd suggest base 251 10) but remember that the fewer bits you use the more "non-unique" and ambiguous the checksum becomes.