Information on Result #879978
Linear OOA(25617, 32772, F256, 2, 8) (dual of [(32772, 2), 65527, 9]-NRT-code), using OOA 2-folding based on linear OA(25617, 65544, F256, 8) (dual of [65544, 65527, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] 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(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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 | Linear OOA(25663, 4227073, F256, 2, 16) (dual of [(4227073, 2), 8454083, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(25666, 4227073, F256, 2, 17) (dual of [(4227073, 2), 8454080, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(25617, 32772, F256, 3, 8) (dual of [(32772, 3), 98299, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(25617, 32772, F256, 4, 8) (dual of [(32772, 4), 131071, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(25617, 32772, F256, 5, 8) (dual of [(32772, 5), 163843, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(25617, 32772, F256, 6, 8) (dual of [(32772, 6), 196615, 9]-NRT-code) | [i] | ||
| 7 | Digital (9, 17, 32772)-net over F256 | [i] | ||