Information on Result #1361840
Linear OOA(2250, 1055, F2, 2, 43) (dual of [(1055, 2), 1860, 44]-NRT-code), using OOA 2-folding based on linear OA(2250, 2110, F2, 43) (dual of [2110, 1860, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [i] based on
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(218, 62, F2, 7) (dual of [62, 44, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(218, 64, F2, 7) (dual of [64, 46, 8]-code), using
- adding a parity check bit [i] based on linear OA(217, 63, F2, 6) (dual of [63, 46, 7]-code), using
- a “cy†code from Brouwer’s database [i]
- adding a parity check bit [i] based on linear OA(217, 63, F2, 6) (dual of [63, 46, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(218, 64, F2, 7) (dual of [64, 46, 8]-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(2250, 1055, F2, 3, 43) (dual of [(1055, 3), 2915, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2250, 1055, F2, 4, 43) (dual of [(1055, 4), 3970, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(2250, 1055, F2, 5, 43) (dual of [(1055, 5), 5025, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(2250, 1055, F2, 6, 43) (dual of [(1055, 6), 6080, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(2250, 1055, F2, 7, 43) (dual of [(1055, 7), 7135, 44]-NRT-code) | [i] | ||
| 6 | Linear OOA(2250, 1055, F2, 8, 43) (dual of [(1055, 8), 8190, 44]-NRT-code) | [i] | ||
| 7 | Digital (207, 250, 1055)-net over F2 | [i] | ||