Search results
Results from the WOW.Com Content Network
A BCH code with = is called a narrow-sense BCH code.; A BCH code with = is called primitive.; The generator polynomial () of a BCH code has coefficients from (). In general, a cyclic code over () with () as the generator polynomial is called a BCH code over ().
Chapter 5 studies cyclic codes and Chapter 6 studies a special case of cyclic codes, the quadratic residue codes. Chapter 7 returns to BCH codes. [1] [6] After these discussions of specific codes, the next chapter concerns enumerator polynomials, including the MacWilliams identities, Pless's own power moment identities, and the Gleason ...
It is used as one of the steps in decoding BCH codes and Reed–Solomon codes (a subclass of BCH codes). George David Forney Jr. developed the algorithm. [1]
Today, Reed–Solomon codes are widely implemented in digital storage devices and digital communication standards, though they are being slowly replaced by Bose–Chaudhuri–Hocquenghem (BCH) codes. For example, Reed–Solomon codes are used in the Digital Video Broadcasting (DVB) standard DVB-S, in conjunction with a convolutional inner code ...
This, as every polynomial code, is indeed a linear code, i.e., linear combinations of code words are again code words. In a case like this where the field is GF(2), linear combinations are found by taking the XOR of the codewords expressed in binary form (e.g. 00111 XOR 10010 = 10101).
Algebraic geometry code; BCH code; BCJR algorithm; Belief propagation; Berger code; Berlekamp–Massey algorithm; Binary Golay code; Binary Goppa code; Bipolar violation; CRHF; Casting out nines; Check digit; Chien's search; Chipkill; Cksum; Coding gain; Coding theory; Constant-weight code; Convolutional code; Cross R-S code; Cryptographic hash ...
A certain family of BCH codes have a particularly useful property, which is that treated as linear operators, their dual operators turns their input into an -wise independent source. That is, the set of vectors from the input vector space are mapped to an ℓ {\displaystyle \ell } -wise independent source.
A negacyclic code is a constacyclic code with λ=-1. [8] A quasi-cyclic code has the property that for some s, any cyclic shift of a codeword by s places is again a codeword. [9] A double circulant code is a quasi-cyclic code of even length with s=2. [9] Quasi-twisted codes and multi-twisted codes are further generalizations of constacyclic ...