Information on Result #1152257
Linear OOA(2246, 18730, F2, 7, 29) (dual of [(18730, 7), 130864, 30]-NRT-code), using OOA 7-folding based on linear OA(2246, 131110, F2, 29) (dual of [131110, 130864, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2246, 131114, F2, 29) (dual of [131114, 130868, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2239, 131073, F2, 29) (dual of [131073, 130834, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2205, 131073, F2, 25) (dual of [131073, 130868, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [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(2246, 18730, F2, 7, 28) (dual of [(18730, 7), 130864, 29]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2247, 18730, F2, 7, 29) (dual of [(18730, 7), 130863, 30]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2248, 18730, F2, 7, 29) (dual of [(18730, 7), 130862, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2246, 18730, F2, 8, 29) (dual of [(18730, 8), 149594, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (217, 246, 18730)-net over F2 | [i] | ||