Information on Result #1444404
Linear OOA(890, 2097186, F8, 2, 14) (dual of [(2097186, 2), 4194282, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(890, 2097186, F8, 14) (dual of [2097186, 2097096, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(889, 2097185, F8, 13) (dual of [2097185, 2097096, 14]-code), using Gilbert–Varšamov bound and bm = 889 > Vbs−1(k−1) = 209153 256979 370980 713353 716128 780870 542763 775821 923133 679432 808138 524142 929933 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-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(890, 1048593, F8, 3, 14) (dual of [(1048593, 3), 3145689, 15]-NRT-code) | [i] | OOA Folding | |