Information on Result #2616316
Linear OOA(2204, 2742, F2, 3, 30) (dual of [(2742, 3), 8022, 31]-NRT-code), using strength reduction based on linear OOA(2204, 2742, F2, 3, 31) (dual of [(2742, 3), 8022, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2204, 8226, F2, 31) (dual of [8226, 8022, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2202, 8224, F2, 31) (dual of [8224, 8022, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2202, 8224, F2, 31) (dual of [8224, 8022, 32]-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(2205, 2742, F2, 3, 30) (dual of [(2742, 3), 8021, 31]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2206, 2742, F2, 3, 30) (dual of [(2742, 3), 8020, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2204, 2204, F2, 4, 30) (dual of [(2204, 4), 8612, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2204, 2204, F2, 5, 30) (dual of [(2204, 5), 10816, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2204, 2204, F2, 6, 30) (dual of [(2204, 6), 13020, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2204, 2204, F2, 7, 30) (dual of [(2204, 7), 15224, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2204, 2204, F2, 8, 30) (dual of [(2204, 8), 17428, 31]-NRT-code) | [i] | ||
| 8 | Digital (174, 204, 2204)-net over F2 | [i] | ||