Information on Result #672830
Linear OA(2242, 4109, F2, 41) (dual of [4109, 3867, 42]-code), using construction X applied to Ce(40) ⊂ Ce(38) 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
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 OA(2242, 4109, F2, 40) (dual of [4109, 3867, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2243, 4110, F2, 41) (dual of [4110, 3867, 42]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2244, 4111, F2, 41) (dual of [4111, 3867, 42]-code) | [i] | ||
| 4 | Linear OA(2245, 4112, F2, 41) (dual of [4112, 3867, 42]-code) | [i] | ||
| 5 | Linear OA(2241, 4108, F2, 40) (dual of [4108, 3867, 41]-code) | [i] | Truncation | |
| 6 | Linear OOA(2242, 2054, F2, 2, 41) (dual of [(2054, 2), 3866, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2242, 1369, F2, 3, 41) (dual of [(1369, 3), 3865, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(2242, 1027, F2, 4, 41) (dual of [(1027, 4), 3866, 42]-NRT-code) | [i] | ||
| 9 | Linear OOA(2242, 821, F2, 5, 41) (dual of [(821, 5), 3863, 42]-NRT-code) | [i] | ||
| 10 | Linear OOA(2242, 684, F2, 6, 41) (dual of [(684, 6), 3862, 42]-NRT-code) | [i] | ||
| 11 | Linear OOA(2242, 587, F2, 7, 41) (dual of [(587, 7), 3867, 42]-NRT-code) | [i] | ||
| 12 | Linear OOA(2242, 513, F2, 8, 41) (dual of [(513, 8), 3862, 42]-NRT-code) | [i] | ||