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Asymmetric Single Magnitude Four Error Correcting Codes.
- Source :
-
IEEE Transactions on Information Theory . Sep2020, Vol. 66 Issue 9, p5322-5334. 13p. - Publication Year :
- 2020
-
Abstract
- Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb {Z}_{2^{k}r}$ which is based on so called $B_{1}[{4}](2^{k}r)$ set. In fact, we reduce the construction of a maximal size $B_{1}[{4}](2^{k}r)$ set for $k\geq 3$ to the construction of a maximal size $B_{1}[{4}](2^{k-3}r)$ set. Finally, we give an explicit formula of a maximal size $B_{1}[{4}](4r)$ set and some lower bounds of a maximal size $B_{1}[{4}](2r)$ set. By computer searching up to $q\leq 106$ , we conjecture that those lower bounds are tight. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 145287376
- Full Text :
- https://doi.org/10.1109/TIT.2020.2977625