Information on Result #686369
Linear OA(8143, 2097224, F8, 21) (dual of [2097224, 2097081, 22]-code), using construction X applied to Ce(20) ⊂ Ce(11) based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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 OOA(8143, 1048612, F8, 2, 21) (dual of [(1048612, 2), 2097081, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8143, 699074, F8, 3, 21) (dual of [(699074, 3), 2097079, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8143, 209722, F8, 21, 21) (dual of [(209722, 21), 4404019, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |