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)