Back to Search
Start Over
Self-Orthogonality Matrix and Reed-Muller Codes.
- Source :
- IEEE Transactions on Information Theory; Nov2022, Vol. 68 Issue 11, p7159-7164, 6p
- Publication Year :
- 2022
-
Abstract
- Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal {C}\,\,(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal {C})$. We extend this result by proposing a new method related to a special matrix, called the self-orthogonality matrix $SO_{k}$ , obtained by shortening a Reed-Muller code ${\mathcal R}(2,k)$. Using this approach, we can extend binary linear codes to many optimal self-orthogonal codes of dimensions 5 and 6. Furthermore, we partially disprove the conjecture (Kim et al. (2021)) by showing that if $31 \le n \le 256$ and $n\equiv 14,22,29 \pmod {31}$ , then there exist optimal $[n], [5]$ codes which are self-orthogonal. We also construct optimal self-orthogonal $[n], [6]$ codes when $41 \le n \le 256$ satisfies $n \ne 46, 54, 61$ and $n \equiv \!\!\!\!\!/~7, 14, 22, 29, 38, 45, 53, 60 \pmod {63}$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 160651163
- Full Text :
- https://doi.org/10.1109/TIT.2022.3186316