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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 ().
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Forney, G. (October 1965), "On Decoding BCH Codes", ...
Each non-zero may be expressed as for some , where is a primitive element of (), is the power number of primitive element . Thus the powers α i {\displaystyle \alpha ^{i}} for 0 ≤ i < ( q − 1 ) {\displaystyle 0\leq i<(q-1)} cover the entire field (excluding the zero element).
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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 ...
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 ...
By 1963 (or possibly earlier), J. J. Stone (and others) recognized that Reed–Solomon codes could use the BCH scheme of using a fixed generator polynomial, making such codes a special class of BCH codes, [4] but Reed–Solomon codes based on the original encoding scheme are not a class of BCH codes, and depending on the set of evaluation ...
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.