Information on Result #880145
Linear OOA(25641, 32778, F256, 2, 18) (dual of [(32778, 2), 65515, 19]-NRT-code), using OOA 2-folding based on linear OA(25641, 65556, F256, 18) (dual of [65556, 65515, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(25641, 32778, F256, 3, 18) (dual of [(32778, 3), 98293, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25641, 32778, F256, 4, 18) (dual of [(32778, 4), 131071, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(25641, 32778, F256, 5, 18) (dual of [(32778, 5), 163849, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(25641, 32778, F256, 6, 18) (dual of [(32778, 6), 196627, 19]-NRT-code) | [i] | ||
| 5 | Digital (23, 41, 32778)-net over F256 | [i] | ||