Information on Result #2667289
Linear OOA(2126, 1371, F2, 3, 21) (dual of [(1371, 3), 3987, 22]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2123, 1370, F2, 3, 21) (dual of [(1370, 3), 3987, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2123, 4110, F2, 21) (dual of [4110, 3987, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2122, 4109, F2, 21) (dual of [4109, 3987, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(20) ⊂ Ce(18) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2122, 4109, F2, 21) (dual of [4109, 3987, 22]-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(2126, 1057, F2, 4, 21) (dual of [(1057, 4), 4102, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2126, 1057, F2, 5, 21) (dual of [(1057, 5), 5159, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2126, 1057, F2, 6, 21) (dual of [(1057, 6), 6216, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2126, 1057, F2, 7, 21) (dual of [(1057, 7), 7273, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2126, 1057, F2, 8, 21) (dual of [(1057, 8), 8330, 22]-NRT-code) | [i] | ||
| 6 | Digital (105, 126, 1057)-net over F2 | [i] | ||