Information on Result #806304
Linear OOA(275, 137, F2, 2, 19) (dual of [(137, 2), 199, 20]-NRT-code), using OOA 2-folding based on linear OA(275, 274, F2, 19) (dual of [274, 199, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(269, 256, F2, 19) (dual of [256, 187, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(257, 256, F2, 15) (dual of [256, 199, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 18, F2, 3) (dual of [18, 12, 4]-code or 18-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(277, 138, F2, 2, 19) (dual of [(138, 2), 199, 20]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(276, 137, F2, 2, 19) (dual of [(137, 2), 198, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(275, 137, F2, 3, 19) (dual of [(137, 3), 336, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(275, 137, F2, 4, 19) (dual of [(137, 4), 473, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(275, 137, F2, 5, 19) (dual of [(137, 5), 610, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(275, 137, F2, 6, 19) (dual of [(137, 6), 747, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(275, 137, F2, 7, 19) (dual of [(137, 7), 884, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(275, 137, F2, 8, 19) (dual of [(137, 8), 1021, 20]-NRT-code) | [i] | ||
| 9 | Digital (56, 75, 137)-net over F2 | [i] | ||