Information on Result #947265
Linear OOA(2209, 2748, F2, 3, 31) (dual of [(2748, 3), 8035, 32]-NRT-code), using OOA 3-folding based on linear OA(2209, 8244, F2, 31) (dual of [8244, 8035, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- 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(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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
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(2210, 2748, F2, 3, 31) (dual of [(2748, 3), 8034, 32]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2209, 2124, F2, 4, 31) (dual of [(2124, 4), 8287, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2209, 2124, F2, 5, 31) (dual of [(2124, 5), 10411, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2209, 2124, F2, 6, 31) (dual of [(2124, 6), 12535, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2209, 2124, F2, 7, 31) (dual of [(2124, 7), 14659, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2209, 2124, F2, 8, 31) (dual of [(2124, 8), 16783, 32]-NRT-code) | [i] | ||
| 7 | Digital (178, 209, 2124)-net over F2 | [i] | ||