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For example, 1011 is encoded (using the non-systematic form of G at the start of this section) into 01 1 0 011 0 where blue digits are data; red digits are parity bits from the [7,4] Hamming code; and the green digit is the parity bit added by the [8,4] code. The green digit makes the parity of the [7,4] codewords even.
Download QR code; Print/export ... (Hamming code). ... For example: The code rate of a convolutional code will typically be 1 ...
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. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correcting codes.
Hamming code; Latin square based code for non-white noise (prevalent for example in broadband over powerlines) Lexicographic code; Linear Network Coding, a type of erasure correcting code across networks instead of point-to-point links; Long code; Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes
He invented the concepts known as Hamming codes, Hamming windows, Hamming numbers, and Hamming distance. In 1972, Nasir Ahmed proposed the discrete cosine transform (DCT), which he developed with T. Natarajan and K. R. Rao in 1973. [2] The DCT is the most widely used lossy compression algorithm, the basis for multimedia formats such as JPEG ...
Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes ...
A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid.
The theory of lexicographic codes is closely connected to combinatorial game theory. In particular, the codewords in a binary lexicographic code of distance d encode the winning positions in a variant of Grundy's game , played on a collection of heaps of stones, in which each move consists of replacing any one heap by at most d − 1 smaller ...