Information on Result #2619867
Linear OOA(2256, 2742, F2, 3, 38) (dual of [(2742, 3), 7970, 39]-NRT-code), using strength reduction based on linear OOA(2256, 2742, F2, 3, 39) (dual of [(2742, 3), 7970, 40]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2256, 8226, F2, 39) (dual of [8226, 7970, 40]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2254, 8224, F2, 39) (dual of [8224, 7970, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- linear OA(2248, 8192, F2, 39) (dual of [8192, 7944, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2254, 8224, F2, 39) (dual of [8224, 7970, 40]-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(2257, 2742, F2, 3, 38) (dual of [(2742, 3), 7969, 39]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2258, 2742, F2, 3, 38) (dual of [(2742, 3), 7968, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(2256, 2303, F2, 4, 38) (dual of [(2303, 4), 8956, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2256, 2303, F2, 5, 38) (dual of [(2303, 5), 11259, 39]-NRT-code) | [i] | ||
| 5 | Linear OOA(2256, 2303, F2, 6, 38) (dual of [(2303, 6), 13562, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(2256, 2303, F2, 7, 38) (dual of [(2303, 7), 15865, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(2256, 2303, F2, 8, 38) (dual of [(2303, 8), 18168, 39]-NRT-code) | [i] | ||
| 8 | Digital (218, 256, 2303)-net over F2 | [i] | ||