Information on Result #699523
Linear OA(8129, 6575, F81, 13) (dual of [6575, 6546, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), 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(8129, 4420, F81, 2, 13) (dual of [(4420, 2), 8811, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8129, 4420, F81, 3, 13) (dual of [(4420, 3), 13231, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(8129, 4420, F81, 4, 13) (dual of [(4420, 4), 17651, 14]-NRT-code) | [i] | ||
| 4 | Digital (16, 29, 4420)-net over F81 | [i] | ||
| 5 | Linear OOA(8129, 3287, F81, 2, 13) (dual of [(3287, 2), 6545, 14]-NRT-code) | [i] | OOA Folding | |