Information on Result #699632
Linear OA(8175, 6599, F81, 32) (dual of [6599, 6524, 33]-code), using construction X applied to Ce(31) ⊂ Ce(18) based on
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(8175, 6599, F81, 2, 32) (dual of [(6599, 2), 13123, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8175, 6599, F81, 3, 32) (dual of [(6599, 3), 19722, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(8175, 6599, F81, 4, 32) (dual of [(6599, 4), 26321, 33]-NRT-code) | [i] | ||
| 4 | Digital (43, 75, 6599)-net over F81 | [i] | ||
| 5 | Linear OOA(8175, 3299, F81, 2, 32) (dual of [(3299, 2), 6523, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8175, 2199, F81, 3, 32) (dual of [(2199, 3), 6522, 33]-NRT-code) | [i] | ||