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2. Hamming code - Wikipedia

   en.wikipedia.org/wiki/Hamming_code

   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 ...

3. Hamming (7,4) - Wikipedia

   en.wikipedia.org/wiki/Hamming(7,4)

   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.

4. Generator matrix - Wikipedia

   en.wikipedia.org/wiki/Generator_matrix

   A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).

5. List of PDF software - Wikipedia

   en.wikipedia.org/wiki/List_of_PDF_software

   Open-source, cross-platform C library to generate PDF files. OpenPDF: GNU LGPLv3 / MPLv2.0: Open source library to create and manipulate PDF files in Java. Fork of an older version of iText, but with the original LGPL / MPL license. PDFsharp: MIT C# developer library to create, extract, edit PDF files. Poppler: GNU GPL

6. Gilbert–Varshamov bound for linear codes - Wikipedia

   en.wikipedia.org/wiki/Gilbert–Varshamov_bound...

   The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements in an error-correcting code of a given block length and minimum Hamming weight over a field . This may be translated into a statement about the maximum rate of a code with given length ...

7. Richard Hamming - Wikipedia

   en.wikipedia.org/wiki/Richard_Hamming

   Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph ...