Information on Result #1053583
Linear OOA(2238, 8206, F2, 4, 30) (dual of [(8206, 4), 32586, 31]-NRT-code), using OOA 4-folding based on linear OA(2238, 32824, F2, 30) (dual of [32824, 32586, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2238, 32825, F2, 30) (dual of [32825, 32587, 31]-code), using
- 1 times truncation [i] based on linear OA(2239, 32826, F2, 31) (dual of [32826, 32587, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 58, F2, 5) (dual of [58, 45, 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(30) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2239, 32826, F2, 31) (dual of [32826, 32587, 32]-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(2238, 6651, F2, 5, 30) (dual of [(6651, 5), 33017, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2238, 6651, F2, 6, 30) (dual of [(6651, 6), 39668, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2238, 6651, F2, 7, 30) (dual of [(6651, 7), 46319, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2238, 6651, F2, 8, 30) (dual of [(6651, 8), 52970, 31]-NRT-code) | [i] | ||
| 5 | Digital (208, 238, 6651)-net over F2 | [i] | ||