ON SOME APPLICATIONS OF ALGEBRA AND GEOMETRY IN CODING THEORY.

Abstract The fundamental problem that led to the development of the theory of error correcting codes was that of having a reliable communication over unreliable channels. A commu- nication channel can be as simple as the air between the voicebox of one adressing an audience and the ears of the listeners. Copper wires connecting telephones or modems can also be considered as channels. In the case of data storage, say in a magnetic tape or disc, the magnetized field in the magnetic tape or disc is the channel. One property of these channels is their capacity to distort the information. For instance, the copper wires connecting telephones may get heated resulting in background interrup- tions. Magnetisation on the tape may re-align over time, or the head of the drive reading the tape or disc may be ill positioned and the right magnetisation be misread! Such distotortions to our good information will be referred to as noise.

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