Information on Result #700311
Linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using construction X applied to Ce(17) ⊂ Ce(16) based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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 OA(1670, 131076, F16, 18) (dual of [131076, 131006, 19]-code) | [i] | Trace Code | |
| 2 | OA(3256, 65538, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6447, 65538, S64, 18) | [i] | ||
| 4 | OA(12840, 65538, S128, 18) | [i] | ||
| 5 | Linear OA(25644, 65795, F256, 18) (dual of [65795, 65751, 19]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25645, 65798, F256, 18) (dual of [65798, 65753, 19]-code) | [i] | ||
| 7 | Linear OA(25646, 65800, F256, 18) (dual of [65800, 65754, 19]-code) | [i] | ||
| 8 | Linear OA(25647, 65802, F256, 18) (dual of [65802, 65755, 19]-code) | [i] | ||
| 9 | Linear OA(25648, 66052, F256, 18) (dual of [66052, 66004, 19]-code) | [i] | ||
| 10 | Linear OA(25649, 66055, F256, 18) (dual of [66055, 66006, 19]-code) | [i] | ||
| 11 | Linear OA(25650, 66313, F256, 18) (dual of [66313, 66263, 19]-code) | [i] | ||
| 12 | Linear OA(25651, 66823, F256, 18) (dual of [66823, 66772, 19]-code) | [i] | ||
| 13 | Linear OOA(25635, 32769, F256, 2, 18) (dual of [(32769, 2), 65503, 19]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(25635, 21846, F256, 3, 18) (dual of [(21846, 3), 65503, 19]-NRT-code) | [i] | ||
| 15 | Linear OOA(25635, 10923, F256, 6, 18) (dual of [(10923, 6), 65503, 19]-NRT-code) | [i] | ||
| 16 | Linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code) | [i] | OA Folding and Stacking | |