A method for deriving tap polynomials of LFSR generating syndromes by using a matrix‐reduction algorithm

Abstract

AbstractThe Berlekamp–Massey method is a method of algebraic error correction in which the key equation, expressing the congruence relation of the received syndrome polynomial, the error locator polynomial, and the error evaluation polynomial, is solved and the error locator polynomial is derived as the shortest LFSR tap polynomial that generates the received syndrome. However, this method is rarely used because of its complex computation process. Consequently, this paper presents a method of deriving the LFSR tap polynomial that generates the received syndrome by the matrix‐reduction method. It is shown that all tap polynomials derived by the matrix‐reduction method have the error locator polynomial as a factor polynomial, and that the factor polynomial is uniquely derived as the error locator polynomial. It is also shown that the matrix‐reduction method is especially useful as a derivation procedure for the error locator polynomial in terms of processing time. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(1): 30–45, 2007; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/ecjc.20234