On the continued fraction and Berlekamp's algorithm (Corresp.)

Continued fraction techniques are equivalent to Berlekamp's algorithm. The sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D(k), k \geq 0</tex> , in Berlekamp's algorithm provides the information about when Berlekamp's algorithm completes one iterative step of the continued fraction. In fact, this happens when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D(K) &lt; k + 1/2</tex> ; and when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D(k) \neq D(k + 1)</tex> , it implies that Berlekamp's algorithm begins the next iterative step of the continued fraction.