Information on Result #880276
Linear OOA(25653, 32781, F256, 2, 23) (dual of [(32781, 2), 65509, 24]-NRT-code), using OOA 2-folding based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(13) [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(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), 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(25653, 32781, F256, 3, 23) (dual of [(32781, 3), 98290, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25653, 32781, F256, 4, 23) (dual of [(32781, 4), 131071, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(25653, 32781, F256, 5, 23) (dual of [(32781, 5), 163852, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(25653, 32781, F256, 6, 23) (dual of [(32781, 6), 196633, 24]-NRT-code) | [i] | ||
| 5 | Digital (30, 53, 32781)-net over F256 | [i] | ||