Shift-register synthesis and BCH decoding

Abstract

It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits. The shit-register approach leads to a simple proof of the validity of the algorithm as well as providing additional insight into its properties. The equivalence of the decoding problem for BCH codes to a shit-register synthesis problem is demonstrated, and other applications for the algorithm are suggested. Cl, c2, * * + , cL are assumed to lie in the same field F, which can be either a finite field GF(q), or an infinite field, such

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“…The algorithm has been checked with five different statistics: monobit, serial, poker, runs, and autocorrelation (see [4]); and with the computation of the linear complexity [1,3]. In table 1 we can see that the results are particularly good.…”

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