Information on Result #945166
Linear OOA(296, 174769, F2, 3, 10) (dual of [(174769, 3), 524211, 11]-NRT-code), using OOA 3-folding based on linear OA(296, 524307, F2, 10) (dual of [524307, 524211, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(296, 524308, F2, 10) (dual of [524308, 524212, 11]-code), using
- 1 times truncation [i] based on linear OA(297, 524309, F2, 11) (dual of [524309, 524212, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(277, 524288, F2, 9) (dual of [524288, 524211, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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
- 1 times truncation [i] based on linear OA(297, 524309, F2, 11) (dual of [524309, 524212, 12]-code), 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(296, 138727, F2, 4, 10) (dual of [(138727, 4), 554812, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(296, 138727, F2, 5, 10) (dual of [(138727, 5), 693539, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(296, 138727, F2, 6, 10) (dual of [(138727, 6), 832266, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(296, 138727, F2, 7, 10) (dual of [(138727, 7), 970993, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(296, 138727, F2, 8, 10) (dual of [(138727, 8), 1109720, 11]-NRT-code) | [i] | ||
| 6 | Digital (86, 96, 138727)-net over F2 | [i] | ||