A decoder includes a syndrome calculator, a Key Equation Solver (KES) and an error corrector. The syndrome calculator receives an n-symbol code word encoded using a Reed Solomon (RS) code to include (nk) redundancy symbols, calculates for the code word 2t syndromes Si, t=(nk)/2 is a maximal number of correctable erroneous symbols. The KES derives an error locator polynomial {circumflex over ()}(x) whose roots identify locations of erroneous symbols, by applying to the syndromes a number of t iterations. In each iteration the KES calculates two discrepancies between {circumflex over ()}(x) and respective two candidates of {circumflex over ()}(x), and derives from the two candidates an updated candidate of {circumflex over ()}(x). The error corrector recovers the code word by correcting the erroneous symbols using the derived error locator polynomial {circumflex over ()}(x).

A decoder includes a syndrome calculator, a Key Equation Solver (KES) and an error corrector. The syndrome calculator is configured to receive an n-symbol code word encoded using a Reed Solomon (RS) code to include (nk) redundancy symbols, and to calculate for the code word 2t syndromes Si, t=(nk)/2 is a maximal number of correctable erroneous symbols. The KES is configured to derive an error locator polynomial (x) whose roots identify locations of erroneous symbols, by applying to the syndromes a number of t iterations. In a single iteration of the t iterations the NES is configured to calculate two discrepancies between (x) and respective two candidates of (x), and to derive from the two candidates an updated candidate of (x). The error corrector is configured to recover the code word by correcting the erroneous symbols using the derived error locator polynomial (x).