Information on Result #1052510
Linear OOA(2137, 2056, F2, 4, 21) (dual of [(2056, 4), 8087, 22]-NRT-code), using OOA 4-folding based on linear OA(2137, 8224, F2, 21) (dual of [8224, 8087, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2137, 8225, F2, 21) (dual of [8225, 8088, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2131, 8193, F2, 21) (dual of [8193, 8062, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2105, 8193, F2, 17) (dual of [8193, 8088, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [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(2137, 2056, F2, 4, 20) (dual of [(2056, 4), 8087, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2138, 2056, F2, 4, 21) (dual of [(2056, 4), 8086, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2139, 2056, F2, 4, 21) (dual of [(2056, 4), 8085, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2137, 2056, F2, 5, 21) (dual of [(2056, 5), 10143, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2137, 2056, F2, 6, 21) (dual of [(2056, 6), 12199, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2137, 2056, F2, 7, 21) (dual of [(2056, 7), 14255, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2137, 2056, F2, 8, 21) (dual of [(2056, 8), 16311, 22]-NRT-code) | [i] | ||
| 8 | Digital (116, 137, 2056)-net over F2 | [i] | ||