or bit summation. The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was...
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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...
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include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph concepts...
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exaggerated way Hamming code, error correction in telecommunication Hamming distance, a way of defining how different two sequences are Hamming weight, the number...
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Enumerator polynomial (redirect from Hamming weight enumerator)
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...
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Bit array (section Population / Hamming weight)
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...
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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...
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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...
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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...
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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...
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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...
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Bar product (section Hamming weight)
{\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 ) =...
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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...
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AN codes (section Arithmetic Weight and Distance)
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}}...
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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...
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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...
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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...
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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...
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Binary code (section Weight of binary codes)
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...
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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...
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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...
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The minimum weight is a concept used in various branches of mathematics and computer science related to measurement. Minimum Hamming weight, a concept...
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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,...
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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...
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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...
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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...
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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...
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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...
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that is, e and λ(n) are coprime. e having a short bit-length and small Hamming weight results in more efficient encryption – the most commonly chosen value...
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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...
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