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DIRECT HARDWARE SOLUTION TO THE QUADRATIC EQUATION y2 + y + c = 0 in GF(2m)

IP.com Disclosure Number: IPCOM000062897D
Original Publication Date: 1985-Jan-01
Included in the Prior Art Database: 2005-Feb-18

Publishing Venue

IBM

Related People

Authors:
Heise, NN Krzystan, TJ [+details]

Abstract

A set of exclusive ORs provides increased error-correcting code decoder performance by a direct hardware solution to the quadratic equation: y2 + y + c = 0 in GF(2m) (1) where GF is Galois Field, and m is any positive integer. Error correction procedure for a Reed-Solomon code involves solving an error locator polynominal for error location vectors. The error locator polynominal is generated from syndromes by distinct matrix operations or Berlekamps algorithm. For a t-error correcting code, the equation is: Xt + s1Xt-1 + . . . + st = 0 (2) Two methods utilized to obtain the roots of this polynominal are: (l) the Chien search, and (2) table lookup. The Chien search is an iterative approach. The table lookup requires that equation (2) be written as a quadratic.