Information on Result #1053096
Linear OOA(2175, 2055, F2, 4, 26) (dual of [(2055, 4), 8045, 27]-NRT-code), using OOA 4-folding based on linear OA(2175, 8220, F2, 26) (dual of [8220, 8045, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2175, 8223, F2, 26) (dual of [8223, 8048, 27]-code), using
- 1 times truncation [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(26) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-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(2175, 2055, F2, 5, 26) (dual of [(2055, 5), 10100, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2175, 2055, F2, 6, 26) (dual of [(2055, 6), 12155, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2175, 2055, F2, 7, 26) (dual of [(2055, 7), 14210, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2175, 2055, F2, 8, 26) (dual of [(2055, 8), 16265, 27]-NRT-code) | [i] | ||
| 5 | Digital (149, 175, 2055)-net over F2 | [i] | ||