Information on Result #731470
Linear OA(9118, 13162, F9, 27) (dual of [13162, 13044, 28]-code), using trace code based on linear OA(8159, 6581, F81, 27) (dual of [6581, 6522, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), 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(9119, 13163, F9, 27) (dual of [13163, 13044, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9118, 6581, F9, 2, 27) (dual of [(6581, 2), 13044, 28]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(9118, 4387, F9, 3, 27) (dual of [(4387, 3), 13043, 28]-NRT-code) | [i] | ||