Information on Result #731321
Linear OA(8170, 8220, F8, 41) (dual of [8220, 8050, 42]-code), using trace code based on linear OA(6485, 4110, F64, 41) (dual of [4110, 4025, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(35) [i] based on
- linear OA(6481, 4096, F64, 41) (dual of [4096, 4015, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(6471, 4096, F64, 36) (dual of [4096, 4025, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), 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, 8221, F8, 41) (dual of [8221, 8050, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8170, 4110, F8, 2, 41) (dual of [(4110, 2), 8050, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8170, 2740, F8, 3, 41) (dual of [(2740, 3), 8050, 42]-NRT-code) | [i] | ||