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Golay Code (other)
Golay code may refer to: * Binary Golay code, an error-correcting code used in digital communications * Ternary Golay code * (Golay) complementary sequences : ''For complementary sequences in biology, see complementarity (molecular biology) In molecular biology, complementarity describes a relationship between two structures each following the lock-and-key principle. In nature complementarity is ... {{mathdab fr:Code de Golay ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Golay Code
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. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing them has been called, by E. R. Berlekamp, the "best single published page" in coding theory. There are two closely related binary Golay codes. The extended binary Golay code, ''G''24 (sometimes just called the "Golay code" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 7-bit errors can be detected. The other, the perfect binary Golay code, ''G''23, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position (conversely, the extended binary Golay code is obtained from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Golay Code
In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is an 1, 6, 53-code, that is, it is a linear code over a ternary alphabet; the relative distance of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a perfect code. The extended ternary Golay code is a 2, 6, 6linear code obtained by adding a zero-sum check digit to the 1, 6, 5code. In finite group theory, the extended ternary Golay code is sometimes referred to as the ternary Golay code. Properties Ternary Golay code The ternary Golay code consists of 36 = 729 codewords. Its parity check matrix is : \left[ \begin 1 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\ 1 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 0 & 0 & 0\\ 1 & 2 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 & 0\\ 1 & 2 & 0 & 1 & 2 & 1 & 0 & 0 & 0 & 1 & 0\\ 1 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \end \right]. Any two different co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementary Sequences
: ''For complementary sequences in biology, see complementarity (molecular biology) In molecular biology, complementarity describes a relationship between two structures each following the lock-and-key principle. In nature complementarity is the base principle of DNA replication and transcription as it is a property shared b .... For integer sequences with complementary sets of members see Lambek–Moser theorem.'' In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for constructing sequences of length 2''N'' and gave examples of complementary sequences of lengths 10 and 26. In 1974 R. J. Turyn gave a method for constructing sequences of length ''mn'' from sequences of lengths ''m'' and ''n'' which allows the construction of sequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
