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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.
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.
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics.
As an example, consider the generator polynomial () = + + + + + +, chosen for use in the (31, 21) binary BCH code used by POCSAG and others. To encode the 21-bit message {101101110111101111101}, we first represent it as a polynomial over ():
Known Barker codes. Here is a table of all known Barker codes, where negations and reversals of the codes have been omitted. A Barker code has a maximum autocorrelation sequence which has sidelobes no larger than 1. It is generally accepted that no other perfect binary phase codes exist.
Definition and parameters. 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.
The sequence of numbers generated by an LFSR or its XNOR counterpart can be considered a binary numeral system just as valid as Gray code or the natural binary code. The arrangement of taps for feedback in an LFSR can be expressed in finite field arithmetic as a polynomial mod 2. This means that the coefficients of the polynomial must be 1s or 0s.
Negation is performed in the finite field Fq. Note that if the characteristic of the underlying field is 2 (i.e., 1 + 1 = 0 in that field), as in binary codes, then - P = P, so the negation is unnecessary. For example, if a binary code has the generator matrix. , then its parity check matrix is. .
A cross compiler can generate binary code for the user machine even if it has a different processor than the machine where the code is compiled. An interpreted program can be distributed as source code.
This is a list of some binary codes that are (or have been) used to represent text as a sequence of binary digits "0" and "1". Fixed-width binary codes use a set number of bits to represent each character in the text, while in variable-width binary codes, the number of bits may vary from character to character.