Information on Result #805478
Linear OOA(253, 4103, F2, 2, 8) (dual of [(4103, 2), 8153, 9]-NRT-code), using OOA 2-folding based on linear OA(253, 8206, F2, 8) (dual of [8206, 8153, 9]-code), using
- 1 times truncation [i] based on linear OA(254, 8207, F2, 9) (dual of [8207, 8153, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(253, 8192, F2, 9) (dual of [8192, 8139, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(240, 8192, F2, 7) (dual of [8192, 8152, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(8) ⊂ Ce(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(2237, 4198404, F2, 2, 16) (dual of [(4198404, 2), 8396571, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2238, 4198404, F2, 2, 17) (dual of [(4198404, 2), 8396570, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(253, 3058, F2, 3, 8) (dual of [(3058, 3), 9121, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(253, 3058, F2, 4, 8) (dual of [(3058, 4), 12179, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(253, 3058, F2, 5, 8) (dual of [(3058, 5), 15237, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(253, 3058, F2, 6, 8) (dual of [(3058, 6), 18295, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(253, 3058, F2, 7, 8) (dual of [(3058, 7), 21353, 9]-NRT-code) | [i] | ||