| Title:
|
$n$-T-quasigroup codes with one check symbol and their error detection capabilities (English) |
| Author:
|
Mullen, Gary L. |
| Author:
|
Shcherbacov, Victor |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
321-340 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $a0\rightarrow 1a$, $a\neq 0$, $a\neq 1$ 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. (English) |
| Keyword:
|
quasigroup |
| Keyword:
|
$n$-ary quasigroup |
| Keyword:
|
check character system |
| Keyword:
|
code |
| Keyword:
|
the system of the serial numbers of German banknotes |
| MSC:
|
20N05 |
| MSC:
|
20N15 |
| MSC:
|
94B60 |
| MSC:
|
94B65 |
| idZBL:
|
Zbl 1099.94036 |
| idMR:
|
MR2075280 |
| . |
| Date available:
|
2009-05-05T16:45:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119461 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
