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  2. Linear code - Wikipedia

    en.wikipedia.org/wiki/Linear_code

    A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.

  3. Reed–Muller code - Wikipedia

    en.wikipedia.org/wiki/Reed–Muller_code

    Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs .

  4. Low-density parity-check code - Wikipedia

    en.wikipedia.org/wiki/Low-density_parity-check_code

    LDPC codes have no limitations of minimum distance, that indirectly means that LDPC codes may be more efficient on relatively large code rates (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2).

  5. Code generation (compiler) - Wikipedia

    en.wikipedia.org/wiki/Code_generation_(compiler)

    Code generation (compiler) In computing, code generation is part of the process chain of a compiler and converts intermediate representation of source code into a form (e.g., machine code) that can be readily executed by the target system. Sophisticated compilers typically perform multiple passes over various intermediate forms.

  6. Microsoft Edge adds autofill coupon codes and more ... - AOL

    www.aol.com/microsoft-edge-adds-autofill-coupon...

    According to Microsoft, Edge will proactively surface the coupon codes at checkout, and from there you can either copy and paste codes, or have Edge try out each code and autofill the one which ...

  7. 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 ...

  8. Parity-check matrix - Wikipedia

    en.wikipedia.org/wiki/Parity-check_matrix

    Definition. Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc⊤ = 0 (some authors [1] would write this in an equivalent form, cH⊤ = 0 .)

  9. BCH code - Wikipedia

    en.wikipedia.org/wiki/BCH_code

    The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code ).

  10. 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.).

  11. Universal Product Code - Wikipedia

    en.wikipedia.org/wiki/Universal_Product_Code

    A UPC barcode. The Universal Product Code (UPC or UPC code) is a barcode symbology that is used worldwide for tracking trade items in stores.. The chosen symbology has bars (or spaces) of exactly 1, 2, 3, or 4 units wide each; each decimal digit to be encoded consists of two bars and two spaces chosen to have a total width of 7 units, in both an "even" and an "odd" parity form, which enables ...

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