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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.
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.
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.
Once the Huffman tree has been generated, it is traversed to generate a dictionary which maps the symbols to binary codes as follows: Start with current node set to the root. If node is not a leaf node, label the edge to the left child as 0 and the edge to the right child as 1 .
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 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 .
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.
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).