Information on Result #699600
Linear OA(8172, 6590, F81, 32) (dual of [6590, 6518, 33]-code), using construction X applied to Ce(31) ⊂ Ce(21) 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(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8172, 4934, F81, 2, 32) (dual of [(4934, 2), 9796, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8172, 4934, F81, 3, 32) (dual of [(4934, 3), 14730, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(8172, 4934, F81, 4, 32) (dual of [(4934, 4), 19664, 33]-NRT-code) | [i] | ||
| 4 | Digital (40, 72, 4934)-net over F81 | [i] | ||
| 5 | Linear OOA(8172, 3295, F81, 2, 32) (dual of [(3295, 2), 6518, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8172, 2196, F81, 3, 32) (dual of [(2196, 3), 6516, 33]-NRT-code) | [i] | ||
| 7 | Linear OOA(8172, 1647, F81, 4, 32) (dual of [(1647, 4), 6516, 33]-NRT-code) | [i] | ||