Information on Result #880123
Linear OOA(25639, 32778, F256, 2, 17) (dual of [(32778, 2), 65517, 18]-NRT-code), using OOA 2-folding based on linear OA(25639, 65556, F256, 17) (dual of [65556, 65517, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(25639, 32778, F256, 3, 17) (dual of [(32778, 3), 98295, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25639, 32778, F256, 4, 17) (dual of [(32778, 4), 131073, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(25639, 32778, F256, 5, 17) (dual of [(32778, 5), 163851, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(25639, 32778, F256, 6, 17) (dual of [(32778, 6), 196629, 18]-NRT-code) | [i] | ||
| 5 | Digital (22, 39, 32778)-net over F256 | [i] | ||