Information on Result #702682
Linear OA(2142, 1062, F2, 26) (dual of [1062, 920, 27]-code), using construction X applied to C([1,26]) ⊂ C([1,20]) based on
- linear OA(2130, 1023, F2, 26) (dual of [1023, 893, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2100, 1023, F2, 20) (dual of [1023, 923, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(212, 39, F2, 5) (dual of [39, 27, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(26, 7, F2, 5) (dual of [7, 1, 6]-code), using
- strength reduction [i] based on linear OA(26, 7, F2, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
- dual of repetition code with length 7 [i]
- strength reduction [i] based on linear OA(26, 7, F2, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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(4) ⊂ Ce(2) [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(2142, 544, F2, 2, 26) (dual of [(544, 2), 946, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2142, 544, F2, 3, 26) (dual of [(544, 3), 1490, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2142, 544, F2, 4, 26) (dual of [(544, 4), 2034, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2142, 544, F2, 5, 26) (dual of [(544, 5), 2578, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(2142, 544, F2, 6, 26) (dual of [(544, 6), 3122, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(2142, 544, F2, 7, 26) (dual of [(544, 7), 3666, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(2142, 544, F2, 8, 26) (dual of [(544, 8), 4210, 27]-NRT-code) | [i] | ||
| 8 | Digital (116, 142, 544)-net over F2 | [i] | ||