In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments. The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream. However, they need to have sufficiently correct codewords for successful reconstruction. Therefore, the existing methods are highly dependent on the channel conditions because a sufficient number of correct codewords should be available for achieving good reconstruction performance. To overcome such high dependency on channel conditions, the proposed blind reconstruction method performs error correction of single-error codewords through the proposed single-error correction method (SCM). Then, both the correct codewords and the corrected single-error codewords are utilized for blind reconstruction. Specifically, the correct codewords are selected based on the algebraic property of BCH and RS codes that codeword polynomials have consecutive roots. At the same time, the codewords presumably with a single error are selected and corrected based on the fact that the most of BCH and RS codeword polynomials with either a single error or double errors do not have consecutive roots. Based on this fact, SCM is devise, which selects and corrects the codewords with a single error with high probability. Finally, it is verified that the proposed blind reconstruction method shows much better reconstruction performance by using only one-tenth of the received codewords compared to the existing best methods even under harsh channel conditions.

中文翻译：

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使用单纠错盲重建 BCH 和 RS 码

本文提出了一种Bose-Chaudhuri-Hocquenghem (BCH)和Reed-Solomon (RS)码的盲重构方法，旨在在非合作环境下从截获的噪声比特流中重构BCH和RS码的生成多项式. 先前的盲重建方法尝试从接收到的比特流中选择正确（或无噪声）的码字或提取码信息。然而，它们需要有足够正确的码字才能成功重建。因此，现有方法高度依赖于信道条件，因为应该有足够数量的正确码字可用于实现良好的重构性能。为了克服对信道条件的高度依赖，所提出的盲重建方法通过所提出的单错误校正方法（SCM）执行单错误码字的错误校正。然后，正确的码字和纠正的单错误码字都被用于盲重建。具体而言，正确的码字是根据BCH和RS码的代数性质选择的，即码字多项式具有连续根。同时，基于大多数具有单错误或双错误的BCH和RS码字多项式不具有连续根的事实，选择并纠正可能具有单个错误的码字。基于这一事实，SCM 被设计出来，它以高概率选择和纠正具有单个错误的码字。最后，