Information on Result #1683726
Linear OOA(2180, 2057, F2, 7, 27) (dual of [(2057, 7), 14219, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2180, 2057, F2, 4, 27) (dual of [(2057, 4), 8048, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2176, 2056, F2, 4, 27) (dual of [(2056, 4), 8048, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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 Ce(26) ⊂ Ce(22) [i] based on
- OOA 4-folding [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-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(2181, 2057, F2, 7, 27) (dual of [(2057, 7), 14218, 28]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2180, 1028, F2, 35, 27) (dual of [(1028, 35), 35800, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |