Information on Result #686984
Linear OA(8153, 32845, F8, 30) (dual of [32845, 32692, 31]-code), using construction X applied to Ce(29) ⊂ Ce(17) based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(822, 77, F8, 11) (dual of [77, 55, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(822, 130, F8, 11) (dual of [130, 108, 12]-code), using
- trace code [i] based on linear OA(6411, 65, F64, 11) (dual of [65, 54, 12]-code or 65-arc in PG(10,64)), using
- extended Reed–Solomon code RSe(54,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- trace code [i] based on linear OA(6411, 65, F64, 11) (dual of [65, 54, 12]-code or 65-arc in PG(10,64)), using
- discarding factors / shortening the dual code based on linear OA(822, 130, F8, 11) (dual of [130, 108, 12]-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(8154, 32846, F8, 30) (dual of [32846, 32692, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8153, 16422, F8, 2, 30) (dual of [(16422, 2), 32691, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8153, 10948, F8, 3, 30) (dual of [(10948, 3), 32691, 31]-NRT-code) | [i] | ||