Name
Abstract | ||
|---|---|---|
In this paper, we study a check digit system which is based on the use of elementary abelian $p$-groups of order $p^{k}$ . This paper is inspired by a recently introduced check digit system for hexadecimal numbers. By interpreting its check equation in terminology of matrix algebra, we generalize the idea to build systems over a group of order $p^{k}$, while keeping the ability to detect all the: 1) single errors; 2) adjacent transpositions; 3) twin errors; 4) jump transpositions; and 5) jump twin errors. Besides, we consider two categories of jump errors: 1) $t$-jump transpositions and 2) $t$-jump twin errors, which include and further extend the double error types of 2)–5). In particular, we explore $R_{c}$, the maximum detection radius of the system on detecting these two kinds of generalized jump errors, and show that it is $2^{k}-2$ for $p=2$ and $(p^{k}-1)/2-1$ for an odd prime $p$. Also, we show how to build such a system that detects all the single errors and these two kinds of double jump-errors within $R_{c}$ . |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/TIT.2013.2287698 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
t-jump transposition,one check digit system,t-jump twin error,error detection,matrix algebra,error detection capability,adjacent transposition,check equation interpretation,maximum detection radius,hexadecimal number,check digit system,double jump-errors type,elementary abelian p-group,elementary abelian group,single error | Prime (order theory),Discrete mathematics,Abelian group,Hexadecimal,Computer science,Matrix algebra,Arithmetic,Algorithm,Error detection and correction,Jump,Check digit | Journal |
Volume | Issue | ISSN |
60 | 1 | 0018-9448 |
Citations | PageRank | References |
1 | 0.60 | 5 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yanling Chen | 1 | 8 | 5.50 |
| Markku Niemenmaa | 2 | 8 | 3.36 |
| a j han vinck | 3 | 419 | 58.77 |
| Danilo Gligoroski | 4 | 193 | 37.59 |