Information on Result #945161
Linear OOA(287, 43697, F2, 3, 10) (dual of [(43697, 3), 131004, 11]-NRT-code), using OOA 3-folding based on linear OA(287, 131091, F2, 10) (dual of [131091, 131004, 11]-code), using
- strength reduction [i] based on linear OA(287, 131091, F2, 11) (dual of [131091, 131004, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(286, 131072, F2, 11) (dual of [131072, 130986, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(269, 131072, F2, 9) (dual of [131072, 131003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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 X4 applied to Ce(10) ⊂ Ce(8) [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(288, 43697, F2, 3, 10) (dual of [(43697, 3), 131003, 11]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(289, 43697, F2, 3, 10) (dual of [(43697, 3), 131002, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(287, 43697, F2, 4, 10) (dual of [(43697, 4), 174701, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(287, 43697, F2, 5, 10) (dual of [(43697, 5), 218398, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(287, 43697, F2, 6, 10) (dual of [(43697, 6), 262095, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(287, 43697, F2, 7, 10) (dual of [(43697, 7), 305792, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(287, 43697, F2, 8, 10) (dual of [(43697, 8), 349489, 11]-NRT-code) | [i] | ||
| 8 | Digital (77, 87, 43697)-net over F2 | [i] | ||