A view of Gaussian elimination applied to early-stopped Berlekamp-Massey algorithm

Chih-Wei Liu*, Chung Chin Lu

*Corresponding author for this work

    Research output: Contribution to journalReview articlepeer-review

    2 Scopus citations


    In this paper, we adopt a restricted Gaussian elimination on the Hankel structured augmented syndrome matrix to reinterpret an early-stopped version of the Berlekamp-Massey algorithm in which only (t + e) iterations are needed to be performed for the decoding of BCH codes up to t errors, where e is the number of errors actually occurred with e ≤ t, instead of the 2t iterations required in the conventional Berlekamp-Massey algorithm. The minimality of (t + e) iterations in this early-stopped Berlekamp-Massey (ESBM) algorithm is justified and related to the subject of simultaneous error correction and detection in this paper. We show that the multiplicative complexity of the ESBM algorithm is upper bounded by (te + e2 - 1) ∀e ≤ t and except for a trivial case, the ESBM algorithm is the most efficient algorithm for finding the error-locator polynomial.

    Original languageEnglish
    Pages (from-to)1131-1143
    Number of pages13
    JournalIEEE Transactions on Communications
    Issue number6
    StatePublished - 1 Jun 2007


    • BCH codes
    • Berlekamp-Massey algorithm
    • Decoding
    • Error-correcting codes
    • Gaussian elimination


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