ABSTRACT
The following fundamental construction yields a lengthening of a given code provided a subcode with a larger minimum distance is known. This has been described as construction X in MacWilliams-Sloane. Rather it describes how the code is embedded in its ambient space Fqn. If readers are interested primarily not in the distance or strength of a code, but in its covering radius, they also speak of a covering code. In order to maximize the minimum distance the codewords have to be spread out such that any two of them are fairly far from each other. In order to minimize the covering radius the codewords have to be placed such that no vector from the ambient space is very far from a codeword. The chapter sketches an amusing link between covering codes and steganography. It is the aim of steganographic techniques to obscure the existence of a message from the adversary.
