Bounds and Constructions for Binary Block Codes Correcting Asymmetric or Unidirectional Errors (Grenzen en Constructies voor Binaire Blokcodes Welke Asymmetrische of Unidirectionel Fouten Verbeteren)

摘要

The thesis deals with error correcting block codes for reliable transmission or storage of data in a communication system using a binary channel. The main object of the thesis is to provide upper and lower bounds on the maximum cardinality of a code of length n which corrects up to t asymmetric or unidirectional errors. It begins by sketching the overall communication system, gives a brief introduction on binary block codes, and treats the symmetric, unidirectional, and asymmetric error types. Further, general conditions for error correction and/or detection capabilities of block codes are derived. Upper bounds on the maximum cardinality of asymmetric or unidirectional error correcting codes are then discussed. Lower bounds on the maximum cardinality of asymmetric or unidirectional error correcting codes can then be obtained by constructing codes. Bounds on the cardinality of codes that are linear are discussed. The appendices give tables with bounds on the maximum number of codewords in a code of length n, as well as tables with bounds on the maximum dimension in a linear code of length n.