Information on Result #731394
Linear OA(978, 13138, F9, 19) (dual of [13138, 13060, 20]-code), using trace code based on linear OA(8139, 6569, F81, 19) (dual of [6569, 6530, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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, 13139, F9, 19) (dual of [13139, 13060, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(978, 13138, F9, 2, 19) (dual of [(13138, 2), 26198, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(978, 13138, F9, 3, 19) (dual of [(13138, 3), 39336, 20]-NRT-code) | [i] | ||
| 4 | Digital (59, 78, 13138)-net over F9 | [i] | ||
| 5 | Linear OOA(978, 6569, F9, 2, 19) (dual of [(6569, 2), 13060, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(978, 4379, F9, 3, 19) (dual of [(4379, 3), 13059, 20]-NRT-code) | [i] | ||