Information on Result #2618854
Linear OOA(2242, 1369, F2, 3, 40) (dual of [(1369, 3), 3865, 41]-NRT-code), using strength reduction based on linear OOA(2242, 1369, F2, 3, 41) (dual of [(1369, 3), 3865, 42]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2242, 4107, F2, 41) (dual of [4107, 3865, 42]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using
Mode: Constructive and 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(2242, 1369, F2, 4, 40) (dual of [(1369, 4), 5234, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2242, 1369, F2, 5, 40) (dual of [(1369, 5), 6603, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(2242, 1369, F2, 6, 40) (dual of [(1369, 6), 7972, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2242, 1369, F2, 7, 40) (dual of [(1369, 7), 9341, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2242, 1369, F2, 8, 40) (dual of [(1369, 8), 10710, 41]-NRT-code) | [i] | ||
| 6 | Digital (202, 242, 1369)-net over F2 | [i] | ||