Information on Result #699490
Linear OA(8142, 6572, F81, 20) (dual of [6572, 6530, 21]-code), using construction X applied to Ce(19) ⊂ Ce(15) based on
- 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(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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 OA(984, 13144, F9, 20) (dual of [13144, 13060, 21]-code) | [i] | Trace Code | |
| 2 | OA(2756, 6572, S27, 20) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(8142, 3286, F81, 2, 20) (dual of [(3286, 2), 6530, 21]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8142, 2190, F81, 3, 20) (dual of [(2190, 3), 6528, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(8142, 1643, F81, 4, 20) (dual of [(1643, 4), 6530, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(8142, 657, F81, 20, 20) (dual of [(657, 20), 13098, 21]-NRT-code) | [i] | OA Folding and Stacking | |