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:<math>g(x) = {\rm lcm}(m_1(x), m_2(x)) = m_1(x) = x^4 + x + 1.\,</math>
It has minimal [[Hamming distance]] at least 3 and corrects up to one error. Since the generator polynomial is of degree 4, this code has 11 data bits and 4 checksum bits. It is also denoted as: '''(15, 11) BCH''' code.
The BCH code with <math>d=4,5</math> has generator polynomial
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\end{align}</math>
It has minimal Hamming distance at least 5 and corrects up to two errors. Since the generator polynomial is of degree 8, this code has 7 data bits and 8 checksum bits. It is also denoted as: '''(15, 7) BCH''' code.
The BCH code with <math>d=6,7</math> has generator polynomial
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\end{align}</math>
It has minimal Hamming distance at least 7 and corrects up to three errors. Since the generator polynomial is of degree 10, this code has 5 data bits and 10 checksum bits. It is also denoted as: '''(15, 5) BCH''' code. (This particular generator polynomial has a real-world application, in the format patterns of the [[QR code]].)
The BCH code with <math>d=8</math> and higher has generator polynomial
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\end{align}</math>
This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: '''(15, 1) BCH''' code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code).
=== General BCH codes ===
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