Information on Result #1517631
Linear OOA(2231, 1016, F2, 3, 40) (dual of [(1016, 3), 2817, 41]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2231, 1016, F2, 2, 40) (dual of [(1016, 2), 1801, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2231, 1042, F2, 2, 40) (dual of [(1042, 2), 1853, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2231, 2084, F2, 40) (dual of [2084, 1853, 41]-code), using
- 1 times truncation [i] based on linear OA(2232, 2085, F2, 41) (dual of [2085, 1853, 42]-code), using
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(2232, 2085, F2, 41) (dual of [2085, 1853, 42]-code), using
- OOA 2-folding [i] based on linear OA(2231, 2084, F2, 40) (dual of [2084, 1853, 41]-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(2231, 508, F2, 5, 40) (dual of [(508, 5), 2309, 41]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2231, 508, F2, 6, 40) (dual of [(508, 6), 2817, 41]-NRT-code) | [i] | ||