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For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
The block length of a block code is the number of symbols in a block. Hence, the elements c {\displaystyle c} of Σ n {\displaystyle \Sigma ^{n}} are strings of length n {\displaystyle n} and correspond to blocks that may be received by the receiver.
The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block length in the sense that all 1-bit errors within that block length have different remainders (also called syndromes) and therefore, since the remainder is a linear function of the block, the code can detect all 2 ...
If the length of the original data is an integer multiple of the block size B, then an extra block of bytes with value B is added. This is necessary so the deciphering algorithm can determine with certainty whether the last byte of the last block is a pad byte indicating the number of padding bytes added or part of the plaintext message.
The padded data comprises (in this order): The length of the unpadded data (in bits) expressed in big-endian binary in n bits (i.e. one cipher block); The unpadded data; As many (possibly none) bits with value 0 as are required to bring the total length to a multiple of n bits
The length of this bit string is the block size. [1] Both the input ( plaintext ) and output ( ciphertext ) are the same length; the output cannot be shorter than the input – this follows logically from the pigeonhole principle and the fact that the cipher must be reversible – and it is undesirable for the output to be longer than the input.
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The following steps describe how to handle the last two blocks of the plaintext, called P n−1 and P n, where the length of P n−1 equals the block size of the cipher in bits, B; the length of the last block, P n, is M bits; and K is the key that is in use. M can range from 1 to B, inclusive, so P n could possibly be a complete block.