Information on Result #700388
Linear OA(25618, 65547, F256, 8) (dual of [65547, 65529, 9]-code), using construction X applied to Ce(7) ⊂ Ce(3) based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), 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(12821, 65547, S128, 8) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25618, 65547, F256, 2, 8) (dual of [(65547, 2), 131076, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25618, 65547, F256, 3, 8) (dual of [(65547, 3), 196623, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(25618, 65547, F256, 4, 8) (dual of [(65547, 4), 262170, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(25618, 65547, F256, 5, 8) (dual of [(65547, 5), 327717, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(25618, 65547, F256, 6, 8) (dual of [(65547, 6), 393264, 9]-NRT-code) | [i] | ||
| 7 | Digital (10, 18, 65547)-net over F256 | [i] | ||
| 8 | Linear OOA(25618, 32773, F256, 2, 8) (dual of [(32773, 2), 65528, 9]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25618, 21849, F256, 3, 8) (dual of [(21849, 3), 65529, 9]-NRT-code) | [i] | ||