Information on Result #880274
Linear OOA(25651, 32778, F256, 2, 23) (dual of [(32778, 2), 65505, 24]-NRT-code), using OOA 2-folding based on linear OA(25651, 65556, F256, 23) (dual of [65556, 65505, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), 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(25651, 25870, F256, 3, 23) (dual of [(25870, 3), 77559, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25651, 25870, F256, 4, 23) (dual of [(25870, 4), 103429, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(25651, 25870, F256, 5, 23) (dual of [(25870, 5), 129299, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(25651, 25870, F256, 6, 23) (dual of [(25870, 6), 155169, 24]-NRT-code) | [i] | ||
| 5 | Digital (28, 51, 25870)-net over F256 | [i] | ||