Information on Result #1630592
Linear OOA(291, 77855, F2, 5, 10) (dual of [(77855, 5), 389184, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(291, 77855, F2, 3, 10) (dual of [(77855, 3), 233474, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(291, 87387, F2, 3, 10) (dual of [(87387, 3), 262070, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(291, 262161, F2, 10) (dual of [262161, 262070, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(291, 262163, F2, 10) (dual of [262163, 262072, 11]-code), using
- 1 times truncation [i] based on linear OA(292, 262164, F2, 11) (dual of [262164, 262072, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(273, 262144, F2, 9) (dual of [262144, 262071, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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 X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(292, 262164, F2, 11) (dual of [262164, 262072, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(291, 262163, F2, 10) (dual of [262163, 262072, 11]-code), using
- OOA 3-folding [i] based on linear OA(291, 262161, F2, 10) (dual of [262161, 262070, 11]-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(291, 77854, F2, 6, 10) (dual of [(77854, 6), 467033, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(291, 77854, F2, 7, 10) (dual of [(77854, 7), 544887, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(291, 77854, F2, 8, 10) (dual of [(77854, 8), 622741, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(291, 77854, F2, 15, 10) (dual of [(77854, 15), 1167719, 11]-NRT-code) | [i] | ||