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n -T-quasigroup codes with one check symbol and their error detection capabilities

Gary L. Mullen, Viktor Alekseevich Shcherbakov (2004)

Commentationes Mathematicae Universitatis Carolinae

It is well known that there exist some types of the most frequent errors made by human operators during transmission of data which it is possible to detect using a code with one check symbol. We prove that there does not exist an n -T-code that can detect all single, adjacent transposition, jump transposition, twin, jump twin and phonetic errors over an alphabet that contains 0 and 1. Systems that detect all single, adjacent transposition, jump transposition, twin, jump twin errors and almost all...

Nonassociative algebras: some applications.

Santos González, Consuelo Martínez (2003)

Revista Matemática Iberoamericana

Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.

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