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Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine. The remaining six values are illegal and ...
The binary Golay code, G 23 is a perfect code. That is, the spheres of radius three around code words form a partition of the vector space. G 23 is a 12-dimensional subspace of the space F 23 2. The automorphism group of the perfect binary Golay code G 23 (meaning the subgroup of the group S 23 of permutations of the coordinates of F 23
The QR code system was invented in 1994, at the Denso Wave automotive products company, in Japan. [5] [6] [7] The initial alternating-square design presented by the team of researchers, headed by Masahiro Hara, was influenced by the black counters and the white counters played on a Go board; [8] the pattern of position detection was found and determined by applying the least-used ratio (1:1:3 ...
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.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
Cyclic redundancy check. A cyclic redundancy check ( CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. [ 1][ 2] Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents.
Pseudorandom binary sequence. A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict [ 1] and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such ...
Burst error-correcting code. In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other. Many codes have been designed to correct random errors.
A binary number is a number expressed in the base -2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one ). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the ...