summation. The Hamming weight is named after the American mathematician Richard Hamming, although he did not originate the notion. The Hamming weight of binary...

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...

coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight. Let C ⊂ F 2 n {\displaystyle...

exaggerated way Hamming code, error correction in telecommunication Hamming distance, a way of defining how different two sequences are Hamming weight, 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...

of 1 bits in a bit array, sometimes called the population count or Hamming weight, there are efficient branch-free algorithms that can compute the number...

constant-weight code, also called an m-of-n code, is an error detection and correction code where all codewords share the same Hamming weight. The one-hot...

number theory, a pernicious number is a positive integer such that the Hamming weight of its binary representation is prime, that is, there is a prime number...

smallest number of non-zero entries, that is, the one with minimal Hamming weight. One method of doing this is to compute the representation in non-adjacent...

The minimum weight is a concept used in various branches of mathematics and computer science related to measurement. Minimum Hamming weight, a concept...

Over GF(2) the AOP has many interesting properties, including: The Hamming weight of the AOP is m + 1, the maximum possible for its degree The AOP is...

Lee weight and Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} with the Hamming weight. Considering the alphabet as the additive group Zq, the Lee distance...

e i g h t ( 11 ) = 2 {\displaystyle {\mathsf {Hamming\_weight}}(01\oplus 10)={\mathsf {Hamming\_weight}}(11)=2} E-Cube routing is a static routing method...

A binary code is called an even code if the Hamming weight 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 Hamming weight of exactly 2 k − 1 {\displaystyle 2^{k-1}} , which implies that the...

{\displaystyle C_{1}\mid C_{2}} . The Hamming weight 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 ) =...

about every member of a population (not necessarily a human population) Hamming weight, the number of non-zero entries ('1' bits) in a byte, string, word,...

elements in an error-correcting code of a given block length and minimum Hamming weight over a field F q {\displaystyle \mathbb {F} _{q}} . This may be translated...

t {\displaystyle t} equal to its hamming weight. The arithmetic weight will usually be less than the hamming weight since the a i {\displaystyle a_{i}}...

voice over IP networks. The weight of a binary code, as defined in the table of constant-weight codes, is the Hamming weight of the binary words coding...

digit sum of the binary representation of a number is known as its Hamming weight or population count; algorithms for performing this operation have been...

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...

all code words have Hamming weights of 0, 8, 12, 16, or 24. Code words of weight 8 are called octads and code words of weight 12 are called dodecads...

an integer divisible by 2 but not divisible by 4 Even code, if the Hamming weight of all of a binary code's codewords is even Even (band), an Australian...

system, as they involve little more than string concatenation. The Hamming weight or population count operation that counts the number of nonzero bits...

doubly even. Type I codes are always even (every codeword has even Hamming weight). Type II codes are binary self-dual codes which are doubly even. Type...

of pointers equal in length to the number of ones in the bitmap (its Hamming weight). The hash array mapped trie achieves almost hash table-like speed while...

σ(n) = n + 1 for all n. A set X of binary strings is called balanced if the Hamming weight of elements of X takes at most two distinct values. That is, for any...

that Hamming balls have the smallest vertex boundary among all sets of a given size. Hamming balls are sets that contain all points of Hamming weight at...

if its truth table contains an equal number of zeros and ones. The Hamming weight of the function is the number of ones in the truth table. Bent: its...