Information on Result #1599189
Linear OOA(2243, 1370, F2, 4, 40) (dual of [(1370, 4), 5237, 41]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2243, 1370, F2, 3, 40) (dual of [(1370, 3), 3867, 41]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2243, 4110, F2, 40) (dual of [4110, 3867, 41]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2241, 4108, F2, 40) (dual of [4108, 3867, 41]-code), using
- 1 times truncation [i] based on linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(38) [i] based on
- linear OA(2241, 4096, F2, 41) (dual of [4096, 3855, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(40) ⊂ Ce(38) [i] based on
- 1 times truncation [i] based on linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2241, 4108, F2, 40) (dual of [4108, 3867, 41]-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(2244, 1370, F2, 4, 40) (dual of [(1370, 4), 5236, 41]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2245, 1370, F2, 4, 40) (dual of [(1370, 4), 5235, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(2243, 685, F2, 7, 40) (dual of [(685, 7), 4552, 41]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2243, 685, F2, 8, 40) (dual of [(685, 8), 5237, 41]-NRT-code) | [i] | ||