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The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ℓ₁ norm of a bit vector. In this binary case, it is also called the population count,[1]popcount, sideways sum,[2] or bit summation.[3]
Examples
String
Hamming weight
11101
4
11101000
4
00000000
0
678012340567
10
Graphs are unavailable due to technical issues. There is more info on Phabricator and on MediaWiki.org.
A plot for the population count (Hamming weight for binary numbers) for (decimal) numbers 0 to 256.[4][5][6]
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or bit summation. The Hammingweight is named after Richard Hamming although he did not originate the notion. The Hammingweight of binary numbers was...
3. 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...
exaggerated way Hamming code, error correction in telecommunication Hamming distance, a way of defining how different two sequences are Hammingweight, the number...
include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph concepts...
coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hammingweight. Let C ⊂ F 2 n {\displaystyle...
of 1 bits in a bit array, sometimes called the population count or Hammingweight, there are efficient branch-free algorithms that can compute the number...
number theory, a pernicious number is a positive integer such that the Hammingweight of its binary representation is prime, that is, there is a prime number...
t {\displaystyle t} equal to its hammingweight. The arithmetic weight will usually be less than the hammingweight since the a i {\displaystyle a_{i}}...
Lee weight and Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} with the Hammingweight. Considering the alphabet as the additive group Zq, the Lee distance...
A binary code is called an even code if the Hammingweight of each of its codewords is even. An even code should have a generator polynomial that include...
code. The Hadamard code is unique in that each non-zero codeword has a Hammingweight of exactly 2 k − 1 {\displaystyle 2^{k-1}} , which implies that the...
{\displaystyle C_{1}\mid C_{2}} . The Hammingweight w of the bar product is the lesser of (a) twice the weight of C1, and (b) the weight of C2: w ( C 1 ∣ C 2 ) =...
smallest number of non-zero entries, that is, the one with minimal Hammingweight. One method of doing this is to compute the representation in non-adjacent...
doubly even. Type I codes are always even (every codeword has even Hammingweight). Type II codes are binary self-dual codes which are doubly even. Type...
Over GF(2) the AOP has many interesting properties, including: The Hammingweight of the AOP is m + 1, the maximum possible for its degree The AOP is...
generates octads from code words of Hammingweight 8 from the extended binary Golay code, one of five different Hammingweights the extended binary Golay code...
voice over IP networks. The weight of a binary code, as defined in the table of constant-weight codes, is the Hammingweight of the binary words coding...
an integer divisible by 2 but not divisible by 4 Even code, if the Hammingweight of all of a binary code's codewords is even Even (band), an Australian...
The minimum weight is a concept used in various branches of mathematics and computer science related to measurement. Minimum Hammingweight, a concept...
about every member of a population (not necessarily a human population) Hammingweight, the number of non-zero entries ('1' bits) in a byte, string, word,...
error-correcting codes. He invented the concepts known as Hamming codes, Hamming windows, Hamming numbers, and Hamming distance. In 1972, Nasir Ahmed proposed the discrete...
digit sum of the binary representation of a number is known as its Hammingweight or population count; algorithms for performing this operation have been...
calculating for each input value a the Hammingweight W {\displaystyle W} (number of nonzero components), and adding weights W ( a ) {\displaystyle W(a)} and...
that Hamming balls have the smallest vertex boundary among all sets of a given size. Hamming balls are sets that contain all points of Hammingweight at...
if its truth table contains an equal number of zeros and ones. The Hammingweight of the function is the number of ones in the truth table. Bent: its...
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