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A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits (which ...
A Barker code or Barker sequence is a finite sequence of N values of +1 and −1, with the ideal autocorrelation property, such that the off-peak (non-cyclic) autocorrelation coefficients. are as small as possible: for all . [1] Only nine Barker sequences [6] are known, all of length N at most 13. [7] Barker 's 1953 paper asked for sequences ...
A generator matrix for the binary Golay code is I A, where I is the 12×12 identity matrix, and A is the complement of the adjacency matrix of the icosahedron. A convenient representation [ edit ] It is convenient to use the " Miracle Octad Generator " format, with co-ordinates in an array of 4 rows, 6 columns.
Type II codes are binary self-dual codes which are doubly even. Type III codes are ternary self-dual codes. Every codeword in a Type III code has Hamming weight divisible by 3. Type IV codes are self-dual codes over F 4. These are again even. Codes of types I, II, III, or IV exist only if the length n is a multiple of 2, 8, 4, or 2 respectively.
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 as in analog-to-information ...
Pseudorandom noise. In cryptography, pseudorandom noise ( PRN [1]) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period.
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 would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations.
Gold code. A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication ( CDMA) [1] and satellite navigation ( GPS ). [2] Gold codes are named after Robert Gold. [3] [4] Gold codes have bounded small cross-correlations within a set, which is useful when multiple devices are broadcasting in the same frequency ...