Information on Result #880220
Linear OOA(25648, 32780, F256, 2, 21) (dual of [(32780, 2), 65512, 22]-NRT-code), using OOA 2-folding based on linear OA(25648, 65560, F256, 21) (dual of [65560, 65512, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), 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(25648, 32780, F256, 3, 21) (dual of [(32780, 3), 98292, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25648, 32780, F256, 4, 21) (dual of [(32780, 4), 131072, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(25648, 32780, F256, 5, 21) (dual of [(32780, 5), 163852, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(25648, 32780, F256, 6, 21) (dual of [(32780, 6), 196632, 22]-NRT-code) | [i] | ||
| 5 | Digital (27, 48, 32780)-net over F256 | [i] | ||