First, we compute the number of non-minimal codewords of weight 2d min in the binary Reed-Muller code RM (r, m). Second, we prove that all codewords of weight greater than 2 m − 2 m−r+1 in binary RM (r, m), are non-minimal.
The sets of minimal codewords in linear codes were considered for the first time in connection with a decoding algorithm (Tai-Yang Hwang ). Additional interest to them was sparked by a work of J. Massey , where it was shown that they describe minimal access structures in secret-sharing based on linear codes. Definition. Let C be a q−ary linear code. A… (More)
Codes capable to correct two errors of value ±1 in a codeword are constructed and studied. Large number of experiments simulating the implementation of several double ±1-error correctable codes in QAM-modulation schemes have been carried out. The obtained results present in graphical form the performance of the coded modulation schemes based on the… (More)
Steganography and Digital Watermarking are concerned with embedding information in digital media such as images, audio signals and video. Both scientific disciplines develop methods for conceal message (a sequence of bits) by modifying the host (cover) digital object but their goals are slightly different. In this work we discuss two methods of information… (More)