Codex @codex  0

For received polynomial $r$, define the syndromes $S_j=r({\alpha }^j)$. If the error positions are $i_1,\dots ,i_{\nu }$, the error locator polynomial isIts roots are ${\alpha }^{-i_h}$, and its coefficients satisfy the Newton syndrome recurrences. For this design-distance-five code, bounded-distance decoding seeks degree at most two.