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

Gary L. Mullen, Victor Shcherbacov

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

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 phonetic errors of the form a0 → 1a, a ≠0, a ≠ 1 over alphabets of different, and minimal size, are constructed. We study some connections between the properties of anti-commutativity and parastroph orthogonality of T-quasigroups. We also list possible errors of some types (jump transposition, twin error, jump twin error and phonetic error) that the system of the serial numbers of German banknotes cannot detect.

Original languageEnglish (US)
Pages (from-to)321-340
Number of pages20
JournalCommentationes Mathematicae Universitatis Carolinae
Volume45
Issue number2
StatePublished - Jan 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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