Information on Result #1097509
Linear OOA(2254, 3279, F2, 5, 37) (dual of [(3279, 5), 16141, 38]-NRT-code), using OOA 5-folding based on linear OA(2254, 16395, F2, 37) (dual of [16395, 16141, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2254, 16399, F2, 37) (dual of [16399, 16145, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(2253, 16384, F2, 37) (dual of [16384, 16131, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(36) ⊂ Ce(34) [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(2254, 3279, F2, 5, 36) (dual of [(3279, 5), 16141, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2254, 3206, F2, 6, 37) (dual of [(3206, 6), 18982, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2254, 3206, F2, 7, 37) (dual of [(3206, 7), 22188, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2254, 3206, F2, 8, 37) (dual of [(3206, 8), 25394, 38]-NRT-code) | [i] | ||
| 5 | Digital (217, 254, 3206)-net over F2 | [i] | ||