Information on Result #1631884
Linear OOA(2127, 3977, F2, 5, 18) (dual of [(3977, 5), 19758, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2127, 3977, F2, 4, 18) (dual of [(3977, 4), 15781, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2127, 4099, F2, 4, 18) (dual of [(4099, 4), 16269, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2127, 16396, F2, 18) (dual of [16396, 16269, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2127, 16398, F2, 18) (dual of [16398, 16271, 19]-code), using
- 1 times truncation [i] based on linear OA(2128, 16399, F2, 19) (dual of [16399, 16271, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 16384, F2, 17) (dual of [16384, 16271, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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 X applied to Ce(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2128, 16399, F2, 19) (dual of [16399, 16271, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2127, 16398, F2, 18) (dual of [16398, 16271, 19]-code), using
- OOA 4-folding [i] based on linear OA(2127, 16396, F2, 18) (dual of [16396, 16269, 19]-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(2127, 1988, F2, 25, 18) (dual of [(1988, 25), 49573, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |