We show that the standard decoding algorithm for BCH codes can be modified to run in time polynomial in the length of the syndrome. This works for BCH codes over any field GF (q), which include Hamming codes in the binary case and Reed-Solomon for the case n = q − 1. BCH codes are handled in detail in many textbooks (e.g., [vL92]); our presentation here is quite terse. For simplicity, we only d...

We derive upper bounds on the components of the distance distribution of duals of BCH codes.

Reduction of delay is a main concern in VLSI (Very Large Scale Integration), throughput of the CODEC is effectively increased. A (15, 7) BCH (Bose ChaudhuriHocquenghem Code) Encoder and Decoder for text message is implemented using Verilog HDL. BCH can corrected double error in any position of 15 bit codeword. Initially each character in a text message is converted into binary data of 7 bits. T...

Based on two recently proposed methods in the literature − the “Ranging Criterion” and the “Generators Ranging Criterion” − new (quasi-orthogonal) even BCH-derived sequences are generated, which are very attractive for (synchronous or quasi-synchronous) CDMA applications. These sequences can be easily generated by a linear shift register generator, adding one extra zero or by a cyclically read ...

In this article, a BCH code-based audio watermarking approach performed in the cepstrum domain is proposed. The technique takes advantage of the attack-invariant feature of the cepstrum domain and the error-correction capability of BCH code to increase the robustness of audio watermarking. In addition, the watermarked audio has very high perceptual quality. A blind watermark detection technique...

In this paper, we investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be quite simplified and quantified if weight distribution of the code is binomial-like. We obtain bounds on t...

In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerror correcting BCH-codes.

Benign cephalic histiocytosis (BCH) is a rare non-Langerhans cell histiocytosis of unknown etiology. Clinically, lesions are characterized by small, red-to-yellow papules distributed mainly on the head, face, neck, and shoulders of infants and children. Histopathological specimens show massive histiocytic infiltration of the superficial dermis. Immunohistochemically, they are positive for CD68,...