At the dawn of the theory of codes
type: Item
instance of: scholarly article
title: At the dawn of the theory of codes
zbMATH Open document ID: 0768.94018
DOI: 10.1007/BF03025254
author: Alexander Barg
published in: The Mathematical Intelligencer
publication date: 1993-05-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94-03
zbMATH DE Number: 168564
zbMATH Keywords: codes detecting single error and single transposition
zbMATH Keywords: decoding of BCH codes
zbMATH Keywords: nonlinear equations over a finite field
zbMATH Keywords: perfect codes
zbMATH Keywords: football pool play systems
zbMATH Keywords: commercial codes
zbMATH Keywords: ternary Golay code
Wikidata QID: Q29396944
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 168564