turkmath.org

Error-correcting codes are a mathematical tool for detecting and correcting errors that occur in information transmission. The basic parameters of a code are its information rate and its relative minimum distance. These parameters describe the error-correcting capability of the code, and they satisfy some more or less obvious bounds. In this talk I will discuss old and new results on such bounds. A basic tool will be algebraic curves over finite fields having many rational points. Following an idea of Goppa, such curves can be used for the construction of powerful codes.