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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 ().
It is used as one of the steps in decoding BCH codes and Reed–Solomon codes (a subclass of BCH codes). ... Handout #28 (PDF), Stanford University, pp. ...
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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 ...
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A natural concept for a decoding algorithm for concatenated codes is to first decode the inner code and then the outer code. For the algorithm to be practical it must be polynomial-time in the final block length. Consider that there is a polynomial-time unique decoding algorithm for the outer code.
Elwyn Berlekamp invented an algorithm for decoding Bose–Chaudhuri–Hocquenghem (BCH) codes. [ 3 ] [ 4 ] James Massey recognized its application to linear feedback shift registers and simplified the algorithm.
BCH code (Bose–Chaudhuri–Hocquenghem code), a code in coding theory; Bachelor of Surgery, a component of some undergraduate medical degrees; Baker–Campbell–Hausdorff formula, in mathematics and Lie group theory; Biosafety Clearing-House, an international mechanism that exchanges information about the movement of genetically modified ...