Information on Result #2258617
Linear OA(2128, 4128, F2, 20) (dual of [4128, 4000, 21]-code), using 2 times code embedding in larger space based on linear OA(2126, 4126, F2, 20) (dual of [4126, 4000, 21]-code), using
- 1 times truncation [i] based on linear OA(2127, 4127, F2, 21) (dual of [4127, 4000, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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(2128, 1376, F2, 3, 20) (dual of [(1376, 3), 4000, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2128, 1032, F2, 4, 20) (dual of [(1032, 4), 4000, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2128, 688, F2, 6, 20) (dual of [(688, 6), 4000, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(2128, 516, F2, 8, 20) (dual of [(516, 8), 4000, 21]-NRT-code) | [i] | ||