Information on Result #879967
Linear OOA(25613, 32769, F256, 2, 7) (dual of [(32769, 2), 65525, 8]-NRT-code), using OOA 2-folding based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(25616, 33026, F256, 2, 7) (dual of [(33026, 2), 66036, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(25617, 65538, F256, 2, 7) (dual of [(65538, 2), 131059, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(25653, 4227070, F256, 2, 14) (dual of [(4227070, 2), 8454087, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(25656, 4227070, F256, 2, 15) (dual of [(4227070, 2), 8454084, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(25624, large, F256, 2, 7) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 6 | Linear OOA(25613, 32769, F256, 3, 7) (dual of [(32769, 3), 98294, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(25613, 32769, F256, 4, 7) (dual of [(32769, 4), 131063, 8]-NRT-code) | [i] | ||
| 8 | Linear OOA(25613, 32769, F256, 5, 7) (dual of [(32769, 5), 163832, 8]-NRT-code) | [i] | ||
| 9 | Linear OOA(25613, 32769, F256, 6, 7) (dual of [(32769, 6), 196601, 8]-NRT-code) | [i] | ||