Berlekamp–Massey algorithm: Difference between revisions

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Changed equality to explicit assignment
Changed some equalities to assignments for clarity.
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Each iteration of the algorithm calculates a discrepancy ''d''. At iteration ''k'' this would be:
 
:<math> d =\gets S_{k} + C_1 \ S_{k-1} + \cdots + C_L \ S_{k-L}.</math>
 
If ''d'' is zero, the algorithm assumes that C(x) and L are correct for the moment, increments ''m'', and continues.
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The x<sup>m</sup> term ''shifts'' B(x) so it follows the syndromes corresponding to 'b'. If the previous update of L occurred on iteration ''j'', then ''m = k - j'', and a recalculated discrepancy would be:
 
:<math> d =\gets S_{k} + C_1 \ S_{k-1} + \cdots - (d/b) (S_{j} + B_1 \ S_{j-1} + \cdots ).</math>
 
This would change a recalculated discrepancy to: