Codes Correcting Limited Patterns of Random Errors Using S-K Metric

Abstract

Abstract Coding is essential in all communications and in all multi-operation devices, and errors do occur. For error control, the method in vogue is to use code words with redundant digits. The number of redundant digits is determined based on two things − the number of messages and the kind of errors that need to be controlled. For efficient coding the redundant digits have to be kept to the minimum. In this paper we introduce the idea of limited error patters while using the code alphabet {0,1, 2,..., 1},mod , q Z = q − q when q > 3. We define limitations of the errors in a position by substitution of the character there by a specified number of other characters, rather than by any other character. This is not possible through Hamming approach, because there a character in an error could be substituted by any other of the q-1 characters. The firm mathematical base is provided by use of a metric from the class of S-K metrics, Hamming metric being one of these. The paper gives upper bounds on the codeword lengths for various kinds of “random limited error patterns”. Examples and discussion bring out the tremendous improvement and generalization of Rao Hamming bound.