Information on Result #686471
Linear OA(8140, 262157, F8, 27) (dual of [262157, 262017, 28]-code), using construction X applied to Ce(26) ⊂ Ce(24) 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(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8141, 262158, F8, 27) (dual of [262158, 262017, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8140, 152639, F8, 2, 27) (dual of [(152639, 2), 305138, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8140, 152639, F8, 3, 27) (dual of [(152639, 3), 457777, 28]-NRT-code) | [i] | ||
| 4 | Digital (113, 140, 152639)-net over F8 | [i] | ||
| 5 | Linear OOA(8140, 131078, F8, 2, 27) (dual of [(131078, 2), 262016, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8140, 87385, F8, 3, 27) (dual of [(87385, 3), 262015, 28]-NRT-code) | [i] | ||