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In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction.
If 00010111 is a valid codeword, applying a right circular shift gives the string 10001011. If the code is cyclic, then 10001011 is again a valid codeword. In general, applying a right circular shift moves the least significant bit (LSB) to the leftmost position, so that it becomes the most significant bit (MSB); the other positions are shifted by 1 to the right.
In coding theory, a cycliccode is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting...
A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital...
quadratic residue code is a type of cycliccode. Examples of quadratic residue codes include the ( 7 , 4 ) {\displaystyle (7,4)} Hamming code over G F ( 2...
for BCH codes. Cycliccodes – every cycliccode is also a polynomial code; a popular example is the CRC code. BCH codes – a family of cycliccodes with high...
shifts of strings in L. If L is a cycliccode, then shift(L) ⊆ L; this is a necessary condition for L being a cyclic language. The operation shift(L) has...
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials...
code sequences. Gold sequence (aka Gold code) JPL sequence (aka JPL code) Kasami, Tadao (1966). Weight Distribution Formula for Some Class of Cyclic Codes...
punctured convolutional code. In GPRS, the Coding Schemes CS-1 to CS-4 specify the number of parity bits generated by the cycliccode and the puncturing rate...
consisting of all basis vectors. (The perfect code is obtained by leaving out ∞.) As a cycliccode: The perfect G23 code can be constructed via the factorization...
punctured convolutional code. The Coding Schemes CS-1 to CS-4 specify the number of parity bits generated by the cycliccode and the puncturing rate of...
an AN code. Cyclic AN codes are a subset of cycliccodes and have the same properties. The Mandelbaum-Barrows Codes are a type of cyclic AN codes introduced...
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of...
product of two polynomials, say xn − 1 = g(x)p(x). When g(x) generates a cycliccode C, then the reciprocal polynomial p∗ generates C⊥, the orthogonal complement...
This is a list of hash functions, including cyclic redundancy checks, checksum functions, and cryptographic hash functions. Adler-32 is often mistaken...
Bucladesine is a cyclic nucleotide derivative which mimics the action of endogenous cAMP and is a phosphodiesterase inhibitor. Bucladesine is a cell permeable...
(HTTP) response status codes. Status codes are issued by a server in response to a client's request made to the server. It includes codes from IETF Request...
In telecommunication technology, a Barker code, or Barker sequence, is a finite sequence of digital values with the ideal autocorrelation property. It...
discusses cycliccodes 1959 – Alexis Hocquenghem, and independently the next year Raj Chandra Bose and Dwijendra Kumar Ray-Chaudhuri, discover BCH codes 1960...
they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes, because they can be generated...
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