Information on Result #731081
Linear OA(7106, 4818, F7, 26) (dual of [4818, 4712, 27]-code), using trace code based on linear OA(4953, 2409, F49, 26) (dual of [2409, 2356, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(4951, 2401, F49, 26) (dual of [2401, 2350, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4945, 2401, F49, 23) (dual of [2401, 2356, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(492, 8, F49, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), 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(7107, 4819, F7, 26) (dual of [4819, 4712, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7106, 2409, F7, 2, 26) (dual of [(2409, 2), 4712, 27]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7106, 1606, F7, 3, 26) (dual of [(1606, 3), 4712, 27]-NRT-code) | [i] | ||