Information on Result #699493
Linear OA(8130, 6572, F81, 14) (dual of [6572, 6542, 15]-code), using construction X applied to Ce(13) ⊂ Ce(9) based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(960, 13144, F9, 14) (dual of [13144, 13084, 15]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8130, 3286, F81, 2, 14) (dual of [(3286, 2), 6542, 15]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8130, 2190, F81, 3, 14) (dual of [(2190, 3), 6540, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(8130, 1643, F81, 4, 14) (dual of [(1643, 4), 6542, 15]-NRT-code) | [i] | ||