Information on Result #1053665
Linear OOA(2202, 2056, F2, 4, 31) (dual of [(2056, 4), 8022, 32]-NRT-code), using OOA 4-folding 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
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(2206, 2057, F2, 4, 31) (dual of [(2057, 4), 8022, 32]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2203, 2056, F2, 4, 31) (dual of [(2056, 4), 8021, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2204, 2056, F2, 4, 31) (dual of [(2056, 4), 8020, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2205, 2056, F2, 4, 31) (dual of [(2056, 4), 8019, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2202, 2031, F2, 5, 31) (dual of [(2031, 5), 9953, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2202, 2031, F2, 6, 31) (dual of [(2031, 6), 11984, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2202, 2031, F2, 7, 31) (dual of [(2031, 7), 14015, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2202, 2031, F2, 8, 31) (dual of [(2031, 8), 16046, 32]-NRT-code) | [i] | ||
| 9 | Digital (171, 202, 2031)-net over F2 | [i] | ||