Information on Result #1514408
Linear OOA(2187, 4259836, F2, 3, 12) (dual of [(4259836, 3), 12779321, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2187, 4259836, F2, 2, 12) (dual of [(4259836, 2), 8519485, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(249, 65535, F2, 2, 6) (dual of [(65535, 2), 131021, 7]-NRT-code), using
- linear OOA(2138, 4194301, F2, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2188, 4259836, F2, 3, 12) (dual of [(4259836, 3), 12779320, 13]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2187, 2129918, F2, 5, 12) (dual of [(2129918, 5), 10649403, 13]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2187, 2129918, F2, 6, 12) (dual of [(2129918, 6), 12779321, 13]-NRT-code) | [i] | ||