Information on Result #699521
Linear OA(8133, 6575, F81, 15) (dual of [6575, 6542, 16]-code), using construction X applied to Ce(14) ⊂ Ce(9) based on
- linear OA(8129, 6561, F81, 15) (dual of [6561, 6532, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), 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(8133, 3527, F81, 2, 15) (dual of [(3527, 2), 7021, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8133, 3527, F81, 3, 15) (dual of [(3527, 3), 10548, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(8133, 3527, F81, 4, 15) (dual of [(3527, 4), 14075, 16]-NRT-code) | [i] | ||
| 4 | Digital (18, 33, 3527)-net over F81 | [i] | ||
| 5 | Linear OOA(8133, 3287, F81, 2, 15) (dual of [(3287, 2), 6541, 16]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8133, 939, F81, 15, 15) (dual of [(939, 15), 14052, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |