Information on Result #1095619
Linear OOA(2150, 52435, F2, 5, 16) (dual of [(52435, 5), 262025, 17]-NRT-code), using OOA 5-folding based on linear OA(2150, 262175, F2, 16) (dual of [262175, 262025, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 262176, F2, 16) (dual of [262176, 262026, 17]-code), using
- 1 times truncation [i] based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-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(2150, 52435, F2, 6, 16) (dual of [(52435, 6), 314460, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2150, 52435, F2, 7, 16) (dual of [(52435, 7), 366895, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2150, 52435, F2, 8, 16) (dual of [(52435, 8), 419330, 17]-NRT-code) | [i] | ||
| 4 | Digital (134, 150, 52435)-net over F2 | [i] | ||