Hadamard-Craigen error correcting codes

This paper presents a block coding scheme based on a new construction of block-circulant Hadamard matrices. We describe this unified construction of Hadamard matrices of order 2^tp where p is any odd number and t≥4 (depends on p), explaining how the block-circulant structure of the matrices contributes to more efficient coding. We introduce HC codes that can be implemented in software with relatively short encoding and decoding times. An HC matrix is compact in that it can be represented in its entirety by its first 2^t-1 rows. Experiments show that the HC(64,7,32) code is better than the BCH(63,7,31) code by 1.5 dB and 2.8 dB over the corresponding uncoded data at SNR of 3 dB.