Binary block codes for correcting asymmetric or unidirectional errors
G. Fang · TU/e Research Portal · 1993
The unidirectional failure properties of some recently developed semiconductor large scale integrated non-volatile memories and magnetic recording systems have provided the basis for a new direction of study in coding theory.Modeling these memories and systems as ideal binary asymmetrie channels, the research reported in this dissertation focuses on the characterization and bounds as well as constructions of error correcting block codes used for these channels.Starting from the notion of asymmetrie distance -a metric suitable for ideal binary asymmetrie channels, upper and lower bounds on the maximum cardinality of a block code of length n which corrects up tot asymmetrie errors are presented.Most of them extend the results whieh were known before toa larger area with respect to the length n and the error correcting capability t, and some of them are improvements of those publisbed in the existing literature.Consiclering the same area of length n and error correcting capability t for codes capable of correcting asymmetrie errors, the improved upper and lower bounds on maximum cardinalities of block codes capable of correcting up to t unidirectional errors are also established.The observation of the differences between asymmetrie error-correcting codes and unidirectional error-correcting codes gives constructions of the latter codes based on the constructionsof the former ones by consiclering some comparable codewords if it is necessary.The uniqueness of binary block codes of length less than 9 and minimum asymmetrie distance 2 is thoroughly investigated.It is shown that up to permutation, the codes of maximum cardinalities for even lengtbs are unique, and the numbers of the non-isomorphic codes for odd lengtbs are simultaneously given.Using the asymmetrie distance metric, the notion of the minimum distanee from a eertaio codeword to all other codewordsis introduced.Upper bounds on such distance for maximum size codes are provided.For the trivia} case and for codes which are unique up to permutation, all such distances are equal to the minimum distance of the code.This also holds IX