Content deleted Content added
use z for the reducing polynomial, to avoid having two meanings for x, following the example in https://web.ntpu.edu.tw/~yshan/BCH_code.pdf |
change definition of primitive element to be α(z) |
||
Line 17:
==== Example ====
Let {{math|''q'' {{=}} 2}} and {{math|''m'' {{=}} 4}} (therefore {{math|''n'' {{=}} 15}}). We will consider different values of {{mvar|d}} for {{math|GF(16) {{=}} GF(2<sup>4</sup>)}} based on the reducing polynomial {{math|''z''<sup>4</sup> + ''z'' + 1}}, using primitive element {{math|''α''(''z'') {{=}} ''z''}}. There are fourteen minimum polynomials {{math|''m''<sub>''i''</sub>(''x'')}} with coefficients in {{math|GF(2)}} satisfying
:<math>m_i\left(\alpha^i\right) \bmod \left(z^4 + z + 1\right) = 0.</math>
| |||