Information on Result #1701256
Linear OOA(2186, 907, F2, 8, 32) (dual of [(907, 8), 7070, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2186, 907, F2, 2, 32) (dual of [(907, 2), 1628, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2186, 1040, F2, 2, 32) (dual of [(1040, 2), 1894, 33]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2182, 1038, F2, 2, 32) (dual of [(1038, 2), 1894, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2182, 2076, F2, 32) (dual of [2076, 1894, 33]-code), using
- 1 times truncation [i] based on linear OA(2183, 2077, F2, 33) (dual of [2077, 1894, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2183, 2077, F2, 33) (dual of [2077, 1894, 34]-code), using
- OOA 2-folding [i] based on linear OA(2182, 2076, F2, 32) (dual of [2076, 1894, 33]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2182, 1038, F2, 2, 32) (dual of [(1038, 2), 1894, 33]-NRT-code), using
Mode: 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(2186, 453, F2, 40, 32) (dual of [(453, 40), 17934, 33]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |