Information on Result #686310
Linear OA(8138, 2097184, F8, 22) (dual of [2097184, 2097046, 23]-code), using construction X applied to Ce(21) ⊂ Ce(17) based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(8139, 2097185, F8, 22) (dual of [2097185, 2097046, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8138, 1821259, F8, 2, 22) (dual of [(1821259, 2), 3642380, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8138, 1821259, F8, 3, 22) (dual of [(1821259, 3), 5463639, 23]-NRT-code) | [i] | ||
| 4 | Digital (116, 138, 1821259)-net over F8 | [i] | ||
| 5 | Linear OOA(8138, 1048592, F8, 2, 22) (dual of [(1048592, 2), 2097046, 23]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8138, 699061, F8, 3, 22) (dual of [(699061, 3), 2097045, 23]-NRT-code) | [i] | ||
| 7 | Linear OOA(8138, 190653, F8, 22, 22) (dual of [(190653, 22), 4194228, 23]-NRT-code) | [i] | OA Folding and Stacking | |