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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 ().
Chapter 3 presents the BCH code over the field (), and Chapter 4 develops the theory of finite fields more generally. [1] [6] 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.
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The code-rate is hence a real number. A low code-rate close to zero implies a strong code that uses many redundant bits to achieve a good performance, while a large code-rate close to 1 implies a weak code. The redundant bits that protect the information have to be transferred using the same communication resources that they are trying to protect.
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 ...
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.