Information on Result #699598
Linear OA(8180, 6590, F81, 36) (dual of [6590, 6510, 37]-code), using construction X applied to Ce(35) ⊂ Ce(25) based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(8180, 4584, F81, 2, 36) (dual of [(4584, 2), 9088, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8180, 4584, F81, 3, 36) (dual of [(4584, 3), 13672, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(8180, 4584, F81, 4, 36) (dual of [(4584, 4), 18256, 37]-NRT-code) | [i] | ||
| 4 | Digital (44, 80, 4584)-net over F81 | [i] | ||
| 5 | Linear OOA(8180, 3295, F81, 2, 36) (dual of [(3295, 2), 6510, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8180, 2196, F81, 3, 36) (dual of [(2196, 3), 6508, 37]-NRT-code) | [i] | ||
| 7 | Linear OOA(8180, 1647, F81, 4, 36) (dual of [(1647, 4), 6508, 37]-NRT-code) | [i] | ||