Information on Result #880334
Linear OOA(25657, 32781, F256, 2, 25) (dual of [(32781, 2), 65505, 26]-NRT-code), using OOA 2-folding based on linear OA(25657, 65562, F256, 25) (dual of [65562, 65505, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(15) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), 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(25657, 32781, F256, 3, 25) (dual of [(32781, 3), 98286, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25657, 32781, F256, 4, 25) (dual of [(32781, 4), 131067, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(25657, 32781, F256, 5, 25) (dual of [(32781, 5), 163848, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(25657, 32781, F256, 6, 25) (dual of [(32781, 6), 196629, 26]-NRT-code) | [i] | ||
| 5 | Digital (32, 57, 32781)-net over F256 | [i] | ||