Information on Result #1152415
Linear OOA(2257, 18727, F2, 7, 31) (dual of [(18727, 7), 130832, 32]-NRT-code), using OOA 7-folding based on linear OA(2257, 131089, F2, 31) (dual of [131089, 130832, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2257, 131090, F2, 31) (dual of [131090, 130833, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2256, 131072, F2, 31) (dual of [131072, 130816, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2239, 131072, F2, 29) (dual of [131072, 130833, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
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(2257, 18727, F2, 7, 30) (dual of [(18727, 7), 130832, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2258, 18727, F2, 7, 31) (dual of [(18727, 7), 130831, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2259, 18727, F2, 7, 31) (dual of [(18727, 7), 130830, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2260, 18727, F2, 7, 31) (dual of [(18727, 7), 130829, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2257, 17607, F2, 8, 31) (dual of [(17607, 8), 140599, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (226, 257, 17607)-net over F2 | [i] | ||