Abstract Algebra: Theory and Applications · Problem 22.5.3

Galois Theory — Thomas Judson

Mathematics — Abstract Algebra · finite-fields-bch-error-correction

Problem

Recall the

(15, 7)

-block BCH code in Example 22.2.6. By Theorem 8.1.13, this code is capable of correcting two errors. Suppose that these errors occur in bits

a_1

and

a_2

. The error-locator polynomial is

s(x) = (x + \omega^{a_1})(x + \omega^{a_2})

. Show that

s(x) = x^2 + s_1 x + \left(s_1^2 + \frac{s_3}{s_1}\right).