Information on Result #806410
Linear OOA(277, 132, F2, 2, 20) (dual of [(132, 2), 187, 21]-NRT-code), using OOA 2-folding based on linear OA(277, 264, F2, 20) (dual of [264, 187, 21]-code), using
- 1 times truncation [i] based on linear OA(278, 265, F2, 21) (dual of [265, 187, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(277, 256, F2, 21) (dual of [256, 179, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(269, 256, F2, 19) (dual of [256, 187, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(20) ⊂ Ce(18) [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(277, 131, F2, 3, 20) (dual of [(131, 3), 316, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(277, 131, F2, 4, 20) (dual of [(131, 4), 447, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(277, 131, F2, 5, 20) (dual of [(131, 5), 578, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(277, 131, F2, 6, 20) (dual of [(131, 6), 709, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(277, 131, F2, 7, 20) (dual of [(131, 7), 840, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(277, 131, F2, 8, 20) (dual of [(131, 8), 971, 21]-NRT-code) | [i] | ||
| 7 | Digital (57, 77, 131)-net over F2 | [i] | ||