Information on Result #1683727
Linear OOA(2180, 2360, F2, 7, 26) (dual of [(2360, 7), 16340, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2180, 2360, F2, 3, 26) (dual of [(2360, 3), 6900, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 2742, F2, 3, 26) (dual of [(2742, 3), 8046, 27]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2178, 2742, F2, 3, 26) (dual of [(2742, 3), 8048, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2178, 2742, F2, 3, 27) (dual of [(2742, 3), 8048, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2178, 8226, F2, 27) (dual of [8226, 8048, 28]-code), using
- 2 times code embedding in larger space [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
- 2 times code embedding in larger space [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- OOA 3-folding [i] based on linear OA(2178, 8226, F2, 27) (dual of [8226, 8048, 28]-code), using
- strength reduction [i] based on linear OOA(2178, 2742, F2, 3, 27) (dual of [(2742, 3), 8048, 28]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2178, 2742, F2, 3, 26) (dual of [(2742, 3), 8048, 27]-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(2180, 1179, F2, 35, 26) (dual of [(1179, 35), 41085, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |