Information on Result #880168
Linear OOA(25642, 32777, F256, 2, 19) (dual of [(32777, 2), 65512, 20]-NRT-code), using OOA 2-folding based on linear OA(25642, 65554, F256, 19) (dual of [65554, 65512, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), 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(25642, 27957, F256, 3, 19) (dual of [(27957, 3), 83829, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25642, 27957, F256, 4, 19) (dual of [(27957, 4), 111786, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(25642, 27957, F256, 5, 19) (dual of [(27957, 5), 139743, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(25642, 27957, F256, 6, 19) (dual of [(27957, 6), 167700, 20]-NRT-code) | [i] | ||
| 5 | Digital (23, 42, 27957)-net over F256 | [i] | ||