Information on Result #808708
Linear OOA(2240, 1056, F2, 2, 41) (dual of [(1056, 2), 1872, 42]-NRT-code), using OOA 2-folding based on linear OA(2240, 2112, F2, 41) (dual of [2112, 1872, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(219, 63, F2, 7) (dual of [63, 44, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
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(2240, 1056, F2, 3, 41) (dual of [(1056, 3), 2928, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2240, 1056, F2, 4, 41) (dual of [(1056, 4), 3984, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(2240, 1056, F2, 5, 41) (dual of [(1056, 5), 5040, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2240, 1056, F2, 6, 41) (dual of [(1056, 6), 6096, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(2240, 1056, F2, 7, 41) (dual of [(1056, 7), 7152, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(2240, 1056, F2, 8, 41) (dual of [(1056, 8), 8208, 42]-NRT-code) | [i] | ||
| 7 | Digital (199, 240, 1056)-net over F2 | [i] | ||