Information on Result #805717
Linear OOA(261, 517, F2, 2, 12) (dual of [(517, 2), 973, 13]-NRT-code), using OOA 2-folding based on linear OA(261, 1034, F2, 12) (dual of [1034, 973, 13]-code), using
- 1 times truncation [i] based on linear OA(262, 1035, F2, 13) (dual of [1035, 973, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- 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(251, 1024, F2, 11) (dual of [1024, 973, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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
- 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(261, 378, F2, 3, 12) (dual of [(378, 3), 1073, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(261, 378, F2, 4, 12) (dual of [(378, 4), 1451, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(261, 378, F2, 5, 12) (dual of [(378, 5), 1829, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(261, 378, F2, 6, 12) (dual of [(378, 6), 2207, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(261, 378, F2, 7, 12) (dual of [(378, 7), 2585, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(261, 378, F2, 8, 12) (dual of [(378, 8), 2963, 13]-NRT-code) | [i] | ||
| 7 | Digital (49, 61, 378)-net over F2 | [i] | ||