Information on Result #699631
Linear OA(8177, 6599, F81, 33) (dual of [6599, 6522, 34]-code), using construction X applied to Ce(32) ⊂ Ce(19) based on
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8112, 38, F81, 12) (dual of [38, 26, 13]-code or 38-arc in PG(11,81)), using
- discarding factors / shortening the dual code based on linear OA(8112, 81, F81, 12) (dual of [81, 69, 13]-code or 81-arc in PG(11,81)), using
- Reed–Solomon code RS(69,81) [i]
- discarding factors / shortening the dual code based on linear OA(8112, 81, F81, 12) (dual of [81, 69, 13]-code or 81-arc in PG(11,81)), 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(8177, 6599, F81, 2, 33) (dual of [(6599, 2), 13121, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8177, 6599, F81, 3, 33) (dual of [(6599, 3), 19720, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(8177, 6599, F81, 4, 33) (dual of [(6599, 4), 26319, 34]-NRT-code) | [i] | ||
| 4 | Digital (44, 77, 6599)-net over F81 | [i] | ||
| 5 | Linear OOA(8177, 3299, F81, 2, 33) (dual of [(3299, 2), 6521, 34]-NRT-code) | [i] | OOA Folding | |