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In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal ...
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 ...
The metric space of length- n binary strings, with the Hamming distance, is known as the Hamming cube; it is equivalent as a metric space to the set of distances between vertices in a hypercube graph. One can also view a binary string of length n as a vector in by treating each symbol in the string as a real coordinate; with this embedding, the ...
Template (C++) Templates are a feature of the C++ programming language that allows functions and classes to operate with generic types. This allows a function or class declaration to reference via a generic variable another different class (built-in or newly declared data type) without creating full declaration for each of these different classes.
Hamming (7,4) In coding theory, Hamming (7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
Curiously recurring template pattern. The curiously recurring template pattern ( CRTP) is an idiom, originally in C++, in which a class X derives from a class template instantiation using X itself as a template argument. [ 1] More generally it is known as F-bound polymorphism, and it is a form of F -bounded quantification .
A block code (specifically a Hamming code) where redundant bits are added as a block to the end of the initial message A continuous convolutional code where redundant bits are added continuously into the structure of the code word. The two main categories of ECC codes are block codes and convolutional codes.
Template method pattern. In object-oriented programming, the template method is one of the behavioral design patterns identified by Gamma et al. [ 1] in the book Design Patterns. The template method is a method in a superclass, usually an abstract superclass, and defines the skeleton of an operation in terms of a number of high-level steps.