Information on Result #808707
Linear OOA(2234, 1047, F2, 2, 41) (dual of [(1047, 2), 1860, 42]-NRT-code), using OOA 2-folding based on linear OA(2234, 2094, F2, 41) (dual of [2094, 1860, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 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
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(2234, 1047, F2, 2, 40) (dual of [(1047, 2), 1860, 41]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2236, 1048, F2, 2, 41) (dual of [(1048, 2), 1860, 42]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2238, 1049, F2, 2, 41) (dual of [(1049, 2), 1860, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2235, 1047, F2, 2, 41) (dual of [(1047, 2), 1859, 42]-NRT-code) | [i] | OOA Duplication | |
| 5 | Linear OOA(2234, 980, F2, 3, 41) (dual of [(980, 3), 2706, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2234, 980, F2, 4, 41) (dual of [(980, 4), 3686, 42]-NRT-code) | [i] | ||
| 7 | Linear OOA(2234, 980, F2, 5, 41) (dual of [(980, 5), 4666, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(2234, 980, F2, 6, 41) (dual of [(980, 6), 5646, 42]-NRT-code) | [i] | ||
| 9 | Linear OOA(2234, 980, F2, 7, 41) (dual of [(980, 7), 6626, 42]-NRT-code) | [i] | ||
| 10 | Linear OOA(2234, 980, F2, 8, 41) (dual of [(980, 8), 7606, 42]-NRT-code) | [i] | ||
| 11 | Digital (193, 234, 980)-net over F2 | [i] | ||