Conjugate roots are pairs of complex roots that occur together in polynomial equations, specifically when the coefficients of the polynomial are real numbers. When a polynomial has a complex root of the form 'a + bi', where 'a' and 'b' are real numbers and 'i' is the imaginary unit, its conjugate 'a - bi' must also be a root. This relationship is essential in the construction of error-correcting codes like BCH codes, as it ensures that codewords have certain symmetrical properties and helps maintain the integrity of the coding process.
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