Information on Result #1132729
Linear OOA(2231, 10928, F2, 6, 29) (dual of [(10928, 6), 65337, 30]-NRT-code), using OOA 6-folding based on linear OA(2231, 65568, F2, 29) (dual of [65568, 65337, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2231, 65569, F2, 29) (dual of [65569, 65338, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2225, 65537, F2, 29) (dual of [65537, 65312, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,14]) ⊂ 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(2231, 10822, F2, 7, 29) (dual of [(10822, 7), 75523, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2231, 10822, F2, 8, 29) (dual of [(10822, 8), 86345, 30]-NRT-code) | [i] | ||
| 3 | Digital (202, 231, 10822)-net over F2 | [i] | ||