3.6 Modifications of Linear Block Codes

To suit a particular application, the parameters n and k may need modifications. An ( n, k) block code can be augmented, expurgated, extended, punctured, lengthened, or shortened. In all cases, the minimum Hamming distance property of the code may change after the modifications. These six basic modifications are briefly explained as follows:

1. Augmenting a code An ( n, k) code may be augmented by adding new codewords. The process increases the number of information symbols without changing the codeword length. This corresponds to increasing the number of rows of the generator matrix. Augmentation has very little to offer in most practical applications.

2. Expurgating a code An ( n, k) code may be expurgated by discarding some of the codewords from the code. This process is the inverse of augmenting a code. It decreases the number of information symbols without changing the codeword length. This corresponds to decreasing the number of rows of the generator matrix.

3. Extending a code An ( n, k) code can be extended by annexing parity-check symbols to every codeword of the code. The additional parity-check symbols are carefully chosen to improve the minimum distance of the code. The process increases the codeword length without changing the number of information symbols. This corresponds to increasing the number of columns of the generator matrix. The most common modification is the addition of a 0 parity-check symbol to every codeword of an ( n,