Information on Result #686769
Linear OA(8137, 32779, F8, 31) (dual of [32779, 32642, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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 OOA(8137, 28638, F8, 2, 31) (dual of [(28638, 2), 57139, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8137, 28638, F8, 3, 31) (dual of [(28638, 3), 85777, 32]-NRT-code) | [i] | ||
| 3 | Digital (106, 137, 28638)-net over F8 | [i] | ||
| 4 | Linear OOA(8137, 16389, F8, 2, 31) (dual of [(16389, 2), 32641, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8137, 10926, F8, 3, 31) (dual of [(10926, 3), 32641, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(8137, 2185, F8, 31, 31) (dual of [(2185, 31), 67598, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |