Information on Result #948332
Linear OOA(2253, 1369, F2, 3, 42) (dual of [(1369, 3), 3854, 43]-NRT-code), using OOA 3-folding based on linear OA(2253, 4107, F2, 42) (dual of [4107, 3854, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(2253, 4108, F2, 42) (dual of [4108, 3855, 43]-code), using
- 1 times truncation [i] based on linear OA(2254, 4109, F2, 43) (dual of [4109, 3855, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- linear OA(2253, 4096, F2, 43) (dual of [4096, 3843, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- 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(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(42) ⊂ Ce(40) [i] based on
- 1 times truncation [i] based on linear OA(2254, 4109, F2, 43) (dual of [4109, 3855, 44]-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(2253, 1369, F2, 4, 42) (dual of [(1369, 4), 5223, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2253, 1369, F2, 5, 42) (dual of [(1369, 5), 6592, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(2253, 1369, F2, 6, 42) (dual of [(1369, 6), 7961, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(2253, 1369, F2, 7, 42) (dual of [(1369, 7), 9330, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(2253, 1369, F2, 8, 42) (dual of [(1369, 8), 10699, 43]-NRT-code) | [i] | ||
| 6 | Digital (211, 253, 1369)-net over F2 | [i] | ||