Geometric augmented product codes

We propose a new simple decomposable code construction technique that generates codes with the full information rate for all of the minimum Hamming distance-4 binary linear block codes of even length greater than or equal to eight. Additionally, some optimal Hamming distance-8 and higher distance codes are obtained with our proposed scheme. A generic trellis structure for the proposed codes was also designed. It is shown that our trellis structures provide lower decoding complexity in comparison to the trellises of some other well-known block codes