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

Mullen, Gary L., and Shcherbakov, Viktor Alekseevich. "$n$-T-quasigroup codes with one check symbol and their error detection capabilities." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 321-340. <http://eudml.org/doc/249383>.

@article{Mullen2004,
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 $a0\rightarrow 1a$, $a\ne 0$, $a\ne 1$ 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.},
author = {Mullen, Gary L., Shcherbakov, Viktor Alekseevich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroup; $n$-ary quasigroup; check character system; code; the system of the serial numbers of German banknotes; -ary quasigroup; check character system; code; phonetic error},
language = {eng},
number = {2},
pages = {321-340},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$n$-T-quasigroup codes with one check symbol and their error detection capabilities},
url = {http://eudml.org/doc/249383},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Mullen, Gary L.
AU - Shcherbakov, Viktor Alekseevich
TI - $n$-T-quasigroup codes with one check symbol and their error detection capabilities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 321
EP - 340
AB - 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 $a0\rightarrow 1a$, $a\ne 0$, $a\ne 1$ 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.
LA - eng
KW - quasigroup; $n$-ary quasigroup; check character system; code; the system of the serial numbers of German banknotes; -ary quasigroup; check character system; code; phonetic error
UR - http://eudml.org/doc/249383
ER -