Information on Result #945496
Linear OOA(272, 345, F2, 3, 15) (dual of [(345, 3), 963, 16]-NRT-code), using OOA 3-folding based on linear OA(272, 1035, F2, 15) (dual of [1035, 963, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(271, 1024, F2, 15) (dual of [1024, 953, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(261, 1024, F2, 13) (dual of [1024, 963, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(272, 345, F2, 4, 15) (dual of [(345, 4), 1308, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(272, 345, F2, 5, 15) (dual of [(345, 5), 1653, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(272, 345, F2, 6, 15) (dual of [(345, 6), 1998, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(272, 345, F2, 7, 15) (dual of [(345, 7), 2343, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(272, 345, F2, 8, 15) (dual of [(345, 8), 2688, 16]-NRT-code) | [i] | ||
| 6 | Digital (57, 72, 345)-net over F2 | [i] | ||