Information on Result #731299
Linear OA(8162, 8232, F8, 38) (dual of [8232, 8070, 39]-code), using trace code based on linear OA(6481, 4116, F64, 38) (dual of [4116, 4035, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(6475, 4096, F64, 38) (dual of [4096, 4021, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(6461, 4096, F64, 31) (dual of [4096, 4035, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), 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(8163, 8233, F8, 38) (dual of [8233, 8070, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8162, 4116, F8, 2, 38) (dual of [(4116, 2), 8070, 39]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8162, 2744, F8, 3, 38) (dual of [(2744, 3), 8070, 39]-NRT-code) | [i] | ||