Information on Result #805709
Linear OOA(249, 132, F2, 2, 12) (dual of [(132, 2), 215, 13]-NRT-code), using OOA 2-folding based on linear OA(249, 264, F2, 12) (dual of [264, 215, 13]-code), using
- 1 times truncation [i] based on linear OA(250, 265, F2, 13) (dual of [265, 215, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(249, 256, F2, 13) (dual of [256, 207, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(241, 256, F2, 11) (dual of [256, 215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
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(249, 132, F2, 3, 12) (dual of [(132, 3), 347, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(249, 132, F2, 4, 12) (dual of [(132, 4), 479, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(249, 132, F2, 5, 12) (dual of [(132, 5), 611, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(249, 132, F2, 6, 12) (dual of [(132, 6), 743, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(249, 132, F2, 7, 12) (dual of [(132, 7), 875, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(249, 132, F2, 8, 12) (dual of [(132, 8), 1007, 13]-NRT-code) | [i] | ||
| 7 | Digital (37, 49, 132)-net over F2 | [i] | ||