Information on Result #686989
Linear OA(8167, 32859, F8, 32) (dual of [32859, 32692, 33]-code), using construction X applied to Ce(32) ⊂ Ce(17) based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(826, 91, F8, 13) (dual of [91, 65, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 130, F8, 13) (dual of [130, 104, 14]-code), using
- trace code [i] based on linear OA(6413, 65, F64, 13) (dual of [65, 52, 14]-code or 65-arc in PG(12,64)), using
- extended Reed–Solomon code RSe(52,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- trace code [i] based on linear OA(6413, 65, F64, 13) (dual of [65, 52, 14]-code or 65-arc in PG(12,64)), using
- discarding factors / shortening the dual code based on linear OA(826, 130, F8, 13) (dual of [130, 104, 14]-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(8167, 16429, F8, 2, 32) (dual of [(16429, 2), 32691, 33]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8167, 10953, F8, 3, 32) (dual of [(10953, 3), 32692, 33]-NRT-code) | [i] | ||