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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.
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.
We will now show a construction and implementation for well-balanced binary Gray codes which allows us to generate an n-digit balanced Gray code for every n. The main principle is to inductively construct an ( n + 2)-digit Gray code G ′ {\displaystyle G'} given an n -digit Gray code G in such a way that the balanced property is preserved.
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.
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a Galois field).
A Barker code or Barker sequence is a finite sequence of N values of +1 and −1, a j for j = 1 , 2 , … , N {\displaystyle a_{j}{\text{ for }}j=1,2,\dots ,N} with the ideal autocorrelation property, such that the off-peak (non-cyclic) autocorrelation coefficients
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1" . The base-2 numeral system is a positional notation with a radix of 2 .
In computing and electronic systems, binary-coded decimal ( BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow).
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.