Information on Result #806015
Linear OOA(278, 268, F2, 2, 16) (dual of [(268, 2), 458, 17]-NRT-code), using OOA 2-folding based on linear OA(278, 536, F2, 16) (dual of [536, 458, 17]-code), using
- 1 times truncation [i] based on linear OA(279, 537, F2, 17) (dual of [537, 458, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(273, 513, F2, 17) (dual of [513, 440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(255, 513, F2, 13) (dual of [513, 458, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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
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(278, 268, F2, 3, 16) (dual of [(268, 3), 726, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(278, 268, F2, 4, 16) (dual of [(268, 4), 994, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(278, 268, F2, 5, 16) (dual of [(268, 5), 1262, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(278, 268, F2, 6, 16) (dual of [(268, 6), 1530, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(278, 268, F2, 7, 16) (dual of [(268, 7), 1798, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(278, 268, F2, 8, 16) (dual of [(268, 8), 2066, 17]-NRT-code) | [i] | ||
| 7 | Digital (62, 78, 268)-net over F2 | [i] | ||