Information on Result #686366
Linear OA(8157, 2097224, F8, 23) (dual of [2097224, 2097067, 24]-code), using construction X applied to Ce(22) ⊂ Ce(13) based on
- linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(816, 72, F8, 8) (dual of [72, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(816, 130, F8, 8) (dual of [130, 114, 9]-code), using
- trace code [i] based on linear OA(648, 65, F64, 8) (dual of [65, 57, 9]-code or 65-arc in PG(7,64)), using
- extended Reed–Solomon code RSe(57,64) [i]
- trace code [i] based on linear OA(648, 65, F64, 8) (dual of [65, 57, 9]-code or 65-arc in PG(7,64)), using
- discarding factors / shortening the dual code based on linear OA(816, 130, F8, 8) (dual of [130, 114, 9]-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 OA(8158, 2097225, F8, 23) (dual of [2097225, 2097067, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8157, 1048612, F8, 2, 23) (dual of [(1048612, 2), 2097067, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8157, 699074, F8, 3, 23) (dual of [(699074, 3), 2097065, 24]-NRT-code) | [i] | ||