Double Error Correcting Long Code

Abstract

This paper introduces a novel binary, long double error correcting, systematic code (8 2 5) that can detect and correct errors up to two bits in the received vector using simple concept of syndrome decoding. The motivation behind the construction of this code is the idea to achieve 100% error correction on the receiver side and to use the encoder/decoder that is simpler than the existing double error correcting codes. By 100% correction we mean that when the two bits of information (k=2) is transmitted simultaneously over the noisy channel and if the two bits are in the error, in the received vector, then this code can detect and correct errors up to two bits thus recovering both the two bits of information. We show that to achieve this we need to choose long code length, maximum of 8 bits (n=8). We present a generator matrix and a parity check matrix to achieve required Hamming distance by using the concept of long code. The paper also presents the performance bounds satisfied by the said code.