Editing BCH code (section)

=== Special cases ===
* A BCH code with <math>c=1</math> is called a ''narrow-sense BCH code''.
* A BCH code with <math>n=q^m-1</math> is called ''primitive''.

The generator polynomial <math>g(x)</math> of a BCH code has coefficients from <math>\mathrm{GF}(q).</math>
In general, a cyclic code over <math>\mathrm{GF}(q^p)</math> with <math>g(x)</math> as the generator polynomial is called a BCH code over <math>\mathrm{GF}(q^p).</math>
The BCH code over <math>\mathrm{GF}(q^m)</math> and generator polynomial <math>g(x)</math> with successive powers of <math>\alpha</math> as roots is one type of [[Reed–Solomon code]] where the decoder (syndromes) alphabet is the same as the channel (data and generator polynomial) alphabet, all elements of <math>\mathrm{GF}(q^m)</math> .<ref>{{Harvnb|Gill|n.d.|p=3}}</ref> The other type of Reed Solomon code is an [[Reed–Solomon error correction#Reed & Solomon's original view: The codeword as a sequence of values|original view Reed Solomon code]] which is not a BCH code.