Information on Result #699991
Linear OA(12817, 16392, F128, 8) (dual of [16392, 16375, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1289, 16384, F128, 5) (dual of [16384, 16375, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), 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 | OA(6420, 16392, S64, 8) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12817, 9807, F128, 2, 8) (dual of [(9807, 2), 19597, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12817, 9807, F128, 3, 8) (dual of [(9807, 3), 29404, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(12817, 9807, F128, 4, 8) (dual of [(9807, 4), 39211, 9]-NRT-code) | [i] | ||
| 5 | Digital (9, 17, 9807)-net over F128 | [i] | ||
| 6 | Linear OOA(12817, 8196, F128, 2, 8) (dual of [(8196, 2), 16375, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12817, 5464, F128, 3, 8) (dual of [(5464, 3), 16375, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(12817, 4098, F128, 4, 8) (dual of [(4098, 4), 16375, 9]-NRT-code) | [i] | ||
| 9 | Linear OOA(12817, 4098, F128, 8, 8) (dual of [(4098, 8), 32767, 9]-NRT-code) | [i] | OA Folding and Stacking | |