Information on Result #731315
Linear OA(8168, 8226, F8, 40) (dual of [8226, 8058, 41]-code), using trace code based on linear OA(6484, 4113, F64, 40) (dual of [4113, 4029, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- linear OA(6479, 4096, F64, 40) (dual of [4096, 4017, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(6467, 4096, F64, 34) (dual of [4096, 4029, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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(8169, 8227, F8, 40) (dual of [8227, 8058, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8168, 4113, F8, 2, 40) (dual of [(4113, 2), 8058, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8168, 2742, F8, 3, 40) (dual of [(2742, 3), 8058, 41]-NRT-code) | [i] | ||