For example, the [ 7, 4, 3 ] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords.
32.
Cyclic codes can be used to correct errors, like Hamming codes as a cyclic codes can be used for correcting single error.
33.
Traditional error correct such as Hamming codes can be applied to the bit string before encoding and transmission on the quantum network.
34.
The parity-check matrix "'H "'of a Hamming code is constructed by listing all columns of length " m " that are pair-wise independent.
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Using the systematic construction for Hamming codes from above, the matrix A is apparent and the systematic form of G is written as
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This is the case in computer memory ( ECC memory ), where bit errors are extremely rare and Hamming codes are widely used.
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So, hamming code is a single error correcting code over GF ( 2 ) with n = 2 ^ m-1 and k = n-m.
38.
The device has Total Dose rating of 300Krad, No Latchup at 120 LET and SEU data of 1.34E-10, by using simple SECDED Hamming code.
39.
As the first class of linear codes developed for error correction purpose, the " Hamming codes " has been widely used in digital communication systems.
40.
Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low.
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