Information on Result #731322
Linear OA(8170, 8208, F8, 42) (dual of [8208, 8038, 43]-code), using trace code based on linear OA(6485, 4104, F64, 42) (dual of [4104, 4019, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(38) [i] based on
- linear OA(6483, 4096, F64, 42) (dual of [4096, 4013, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(6477, 4096, F64, 39) (dual of [4096, 4019, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), 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(8171, 8209, F8, 42) (dual of [8209, 8038, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8170, 4104, F8, 2, 42) (dual of [(4104, 2), 8038, 43]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8170, 2736, F8, 3, 42) (dual of [(2736, 3), 8038, 43]-NRT-code) | [i] | ||