Information on Result #686601
Linear OA(8144, 262168, F8, 27) (dual of [262168, 262024, 28]-code), using construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(21) based on
- linear OA(8139, 262144, F8, 27) (dual of [262144, 262005, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(84, 23, F8, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,8)), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(8144, 212898, F8, 2, 27) (dual of [(212898, 2), 425652, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8144, 212898, F8, 3, 27) (dual of [(212898, 3), 638550, 28]-NRT-code) | [i] | ||
| 3 | Digital (117, 144, 212898)-net over F8 | [i] | ||
| 4 | Linear OOA(8144, 131084, F8, 2, 27) (dual of [(131084, 2), 262024, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8144, 87389, F8, 3, 27) (dual of [(87389, 3), 262023, 28]-NRT-code) | [i] | ||