Information on Result #731393
Linear OA(978, 13150, F9, 18) (dual of [13150, 13072, 19]-code), using trace code based on linear OA(8139, 6575, F81, 18) (dual of [6575, 6536, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), 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(979, 13151, F9, 18) (dual of [13151, 13072, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(978, 6575, F9, 2, 18) (dual of [(6575, 2), 13072, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(978, 4383, F9, 3, 18) (dual of [(4383, 3), 13071, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(978, 1461, F9, 18, 18) (dual of [(1461, 18), 26220, 19]-NRT-code) | [i] | OA Folding and Stacking | |