1. Optimal $q$ -Ary Error Correcting/All Unidirectional Error Detecting Codes.
- Author
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Chee, Yeow Meng and Zhang, Xiande
- Subjects
- *
ERROR detection (Information theory) , *ERROR correction (Information theory) , *CODING theory , *COMBINATORICS , *INFORMATION theory - Abstract
Codes that can correct up to $t$ symmetric errors and detect all unidirectional errors, known as $t$ -EC-AUED codes, are studied in this paper. Given positive integers $q$ , $a$ , and $t$ , let $n_{q}(a,t+1)$ denote the length of the shortest $q$ -ary $t$ -EC-AUED code of size $a$. We introduce combinatorial constructions for $q$ -ary $t$ -EC-AUED codes via one-factorizations of complete graphs, and concatenation of MDS codes and codes from resolvable set systems. Consequently, we determine the exact values of $n_{q}(a,t+1)$ for several new infinite families of $q,a$ , and $t$. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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