THE ERROR-CORRECTING PAIR FOR DIRECT SUM CODES

The error-correcting pair is a general algebraic decoding method for linear codes, which exists for many classical linear codes. In this paper, we focus our study on the error-correcting pair for the direct sum code of two linear codes with an error-correcting pair. Firstly, for the direct sum code C of two linear codes with an error-correcting pair, several sufficient conditions for C with an error-correcting pair are given. Secondly, for the direct sum code C of two Maximal Distance Separable linear codes, two Near -Maximal Distance Separable linear codes, or a Maximal Distance Separable linear code and a Near -Maximal Distance Separable linear code, several sufficient conditions for C with an error-correcting pair are given, respectively. And then, we introduce the corresponding decoding procedure of the direct sum code with an error correcting pair, and give several examples.

Automated summary

This paper studies the error-correcting pair for linear codes, focusing on the direct sum code of two linear codes. It provides conditions for the direct sum code to have an error-correcting pair, and discusses the decoding procedure with several examples.