Correction and Weight Distribution of Periodic Random Errors

Abstract

In data transmission and processing, error-correcting codes are used to protect the data from errors during communication. As the transmission channels are accompanied with predominant error patterns, we need to apply appropriate codes for an appropriate channel. In this paper, we consider a particular type of error “periodic random error" and obtain necessary and sufficient conditions for the existence of linear codes correcting such errors. We also obtain the Hamming weight distribution of such an error pattern and derive an upper bound on the total Hamming weight of all codewords on such error correcting codes.