Samsung Electronics Co., Ltd.

Elik Almog Sheffi

Amit Berman

Yaron Shany

Avner Dor

Ariel Doubchak

A method of performing division operations in an error correction code includes the steps of receiving an output &#x3c9;&#x2208;F&#x2020;{0} wherein F=GF(2) is a Galois field of 2elements, &#x3c9;=&#x3a3;&#x3b2;&#xd7;&#x3b1;wherein &#x3b1; is a fixed primitive element of F, and &#x3b2;&#x2208;GF(2), wherein K=GF(2) is a subfield of F, and {1, &#x3b1;} is a basis of F in a linear subspace of K; choosing a primitive element &#x3b4;&#x2208;K, wherein &#x3c9;=&#x3c9;+&#x3b1;&#xd7;&#x3c9;, &#x3c9;=&#x3a3;&#x3b3;&#xd7;&#x3b4;&#x2208;K, &#x3c9;=&#x3a3;&#x3b3;&#xd7;&#x3b4;&#x2208;K, and &#x3b3;=[&#x3b3;, . . . , &#x3b3;]&#x2208;GF(2); accessing a first table with &#x3c9;to obtain &#x3c9;=&#x3c9;, computing &#x3c9;&#xd7;&#x3c9;in field K, accessing a second table with &#x3c9;=&#x3c9;to obtain (1+&#x3b1;&#xd7;&#x3c9;&#xd7;&#x3c9;)=&#x3c9;+&#x3b1;&#xd7;&#x3c9;, wherein &#x3c9;=(&#x3c9;&#xd7;(1+&#x3b1;&#xd7;&#x3c9;&#xd7;&#x3c9;))=&#x3c9;&#xd7;(&#x3c9;+&#x3b1;&#xd7;&#x3c9;)=&#x3c9;&#xd7;&#x3c9;+&#x3b1;&#xd7;&#x3c9;&#xd7;&#x3c9;; and computing products &#x3c9;&#xd7;&#x3c9;and &#x3c9;&#xd7;&#x3c9;to obtain &#x3c9;=&#x3a3;&#x3b8;&#xd7;&#x3b4;+&#x3b1;&#xb7;&#x3a3;&#x3b8;=&#x3b4;where &#x3b8;&#x2208;GF(2).

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Ramat Gan, Israel

Elik Almog Sheffi