Abstract
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for projective dimensions of at most 7, i.e., affine dimensions of at most 8. We obtain several improvements of the bounds and perform two classifications of optimal subspace codes, which are unknown so far in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 817-839 |
| Number of pages | 23 |
| Journal | Advances in Mathematics of Communications |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Nov 2018 |
| MoE publication type | A1 Journal article-refereed |
Funding
The authors were supported by the DFG project "Ganzzahlige Optimierungsmodelle fur Subspace Codes und endliche Geometrie" (DFG grants KU 2430/3-1, WA 1666/9-1).
Keywords
- Galois geometry
- network coding
- subspace code
- partial spread
- NETWORK ERROR-CORRECTION
- CODING THEORY
- LOWER BOUNDS
- DIMENSION
- DISTANCE
- DESIGNS