Correctable Errors of Weight Half the Minimum Distance Plus One for the First-Order Reed-Muller Codes
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چکیده
The number of correctable/uncorrectable errors of weight half the minimum distance plus one for the first-order Reed-Muller codes is determined. From a cryptographic viewpoint, this result immediately leads to the exact number of Boolean functions of m variables with nonlinearity 2m−2 + 1. The notion of larger half and trial set , which is introduced by Helleseth, Kløve, and Levenshtein to describe the monotone structure of correctable/uncorrectable errors, plays a significant role in the result.
منابع مشابه
Correctable Errors of Weight Half the Minimum Distance for the First-Order Reed-Muller Codes
The number of correctable errors of weight half the minimum distance is given for the first-order binary Reed-Muller codes. It is shown that the size of trial set, which is introduced by Helleseth et al. and can be used for a minimum distance decoding or estimating the number of uncorrectable errors, for the first-order Reed-Muller codes is at least that of minimal codewords except for small code
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