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Learn how Hamming (7,4) encodes four bits of data into seven bits by adding three parity bits to detect and correct single-bit errors. See the code generator matrix, the parity-check matrix, and the Venn diagram of the overlapping parity coverage.
Hamming codes are linear error-correcting codes that can detect and correct one-bit errors. Learn how they work, how they differ from parity and repetition codes, and how they are used in computer memory and telecommunication.
A generator matrix is a matrix whose rows form a basis for a linear code. Learn the definition, format, standard form, equivalence, and parity check matrix of a generator matrix in coding theory.
BCH codes are cyclic error-correcting codes constructed using polynomials over a finite field. They can correct multiple bit errors and are used in various applications such as satellite communications, CDs, DVDs and QR codes.
There also exists a Las Vegas construction that takes a random linear code and checks if this code has good Hamming distance, but this construction also has an exponential runtime. For sufficiently large non-prime q and for certain ranges of the variable δ, the Gilbert–Varshamov bound is surpassed by the Tsfasman–Vladut–Zink bound .
A binary Golay code is a linear error-correcting code used in digital communications. It has two types: the extended binary Golay code G24 and the perfect binary Golay code G23, both related to the Mathieu groups and the Steiner system S(5,8,24).
A comprehensive table of computer monitor, television, digital film, and other graphics display resolutions that are in common use. The table shows the resolution type, designation, usage, width, height, aspect ratio, and total pixels for each resolution.
A parity-check matrix is a matrix that describes the linear relations of a linear block code. It can be used to check and decode codewords, and its minimum distance is the minimum number of linearly independent columns.