Information on Result #2668624
Linear OOA(2237, 2748, F2, 3, 34) (dual of [(2748, 3), 8007, 35]-NRT-code), using 22 times duplication based on linear OOA(2235, 2748, F2, 3, 34) (dual of [(2748, 3), 8009, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2235, 8244, F2, 34) (dual of [8244, 8009, 35]-code), using
- strength reduction [i] based on linear OA(2235, 8244, F2, 35) (dual of [8244, 8009, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [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(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(213, 52, F2, 5) (dual of [52, 39, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- strength reduction [i] based on linear OA(2235, 8244, F2, 35) (dual of [8244, 8009, 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(2237, 2641, F2, 4, 34) (dual of [(2641, 4), 10327, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 2641, F2, 5, 34) (dual of [(2641, 5), 12968, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 2641, F2, 6, 34) (dual of [(2641, 6), 15609, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 2641, F2, 7, 34) (dual of [(2641, 7), 18250, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2237, 2641, F2, 8, 34) (dual of [(2641, 8), 20891, 35]-NRT-code) | [i] | ||
| 6 | Digital (203, 237, 2641)-net over F2 | [i] | ||