Information on Result #2668621
Linear OOA(2231, 2742, F2, 3, 34) (dual of [(2742, 3), 7995, 35]-NRT-code), using 21 times duplication based on linear OOA(2230, 2742, F2, 3, 34) (dual of [(2742, 3), 7996, 35]-NRT-code), using
- strength reduction [i] based on linear OOA(2230, 2742, F2, 3, 35) (dual of [(2742, 3), 7996, 36]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2230, 8226, F2, 35) (dual of [8226, 7996, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2228, 8224, F2, 35) (dual of [8224, 7996, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 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(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(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2228, 8224, F2, 35) (dual of [8224, 7996, 36]-code), using
- OOA 3-folding [i] based on linear OA(2230, 8226, F2, 35) (dual of [8226, 7996, 36]-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(2231, 2293, F2, 4, 34) (dual of [(2293, 4), 8941, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2231, 2293, F2, 5, 34) (dual of [(2293, 5), 11234, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2231, 2293, F2, 6, 34) (dual of [(2293, 6), 13527, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2231, 2293, F2, 7, 34) (dual of [(2293, 7), 15820, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2231, 2293, F2, 8, 34) (dual of [(2293, 8), 18113, 35]-NRT-code) | [i] | ||
| 6 | Digital (197, 231, 2293)-net over F2 | [i] | ||