Information on Result #1096077
Linear OOA(2157, 6560, F2, 5, 21) (dual of [(6560, 5), 32643, 22]-NRT-code), using OOA 5-folding based on linear OA(2157, 32800, F2, 21) (dual of [32800, 32643, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2157, 32801, F2, 21) (dual of [32801, 32644, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2151, 32769, F2, 21) (dual of [32769, 32618, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2121, 32769, F2, 17) (dual of [32769, 32648, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, 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(2157, 6560, F2, 6, 21) (dual of [(6560, 6), 39203, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2157, 6560, F2, 7, 21) (dual of [(6560, 7), 45763, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2157, 6560, F2, 8, 21) (dual of [(6560, 8), 52323, 22]-NRT-code) | [i] | ||
| 4 | Digital (136, 157, 6560)-net over F2 | [i] | ||