At the dawn of the theory of codes
We consider three problems in coding theory in a historical-mathematical context. These problems are: construction of codes detecting single error and single transposition, decoding of BCH codes and a system of nonlinear equations over a finite field, and using perfect codes as football pool play systems. For the first problem, we discuss bounds to the size of these codes and heuristic constructions of commercial codes suggested in the beginning of our century. The discussion of the second problem is focused on a system of nonlinear equations that was independently considered by de Prony in 1790s, S. Ramanujan in 1911, and by coding theorists in the early 60s. Finally, we describe the discovery of the ternary Golay code as a good football pool system 2 years before it has been published by M. Golay himself.
codes detecting single error and single transposition
scientific article; zbMATH DE number 168564
scientific article