Abstract Algebra: Theory and Applications · Problem 22.5.2

Galois Theory — Thomas Judson

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

Problem

Show that

s_i = w(\omega^i) = e(\omega^i) = \omega^{ia_1} + \omega^{ia_2} + \cdots + \omega^{ia_k}

for

i = 1, \ldots, 2r

. The error-locator polynomial is defined to be

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