Hamming weight

Hamming weight

Error Control Coding

Published in Jerry D. Gibson, Mobile Communications Handbook, 2017

As noted above, error control codes make it easier to differentiate between different “valid” transmitted signals. With regard to block codes, this property is captured (to first order) by the code's minimum distance, which is defined as the fewest number of coordinates in which two codewords differ. (So the trivial code in the introduction is a (3,1) code with a minimum distance of dmin = 3, because every pair of codewords—and there are only two codewords—differ in at least three coordinates.) The Hamming distance between any two n-tuples is defined as the number of coordinates in which they differ, and the Hamming weight of a particular vector is the number of its nonzero components.

The Restricted Congruences Toolbox

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Published in Khodakhast Bibak, Restricted Congruences in Computing, 2020

Khodakhast Bibak

The Hamming weight of a string over an alphabet is defined as the number of non-zero symbols in the string. For example, the Hamming weight of 01010 is 2, and the number of codewords in VT0(5) with Hamming weight 2 is 2.

Leveraging the power of quantum computing for breaking RSA encryption

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Journal Information

Published in Cyber-Physical Systems, 2021

Moolchand Sharma, Vikas Choudhary, R. S. Bhatia, Sahil Malik, Anshuman Raina, Harshit Khandelwal

‘e’ having a short bit-length and small Hamming weight results in more efficient encryption – most commonly e = 216 + 1 = 65,537. However, the smaller the value of e (such as 3), the less secure the system. e is considered as the public key exponent. d is kept secret as the private key exponent.

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