Information on Result #731083
Linear OA(7108, 4824, F7, 26) (dual of [4824, 4716, 27]-code), using trace code based on linear OA(4954, 2412, F49, 26) (dual of [2412, 2358, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(4943, 2401, F49, 22) (dual of [2401, 2358, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), 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(7109, 4825, F7, 26) (dual of [4825, 4716, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7108, 2412, F7, 2, 26) (dual of [(2412, 2), 4716, 27]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(7108, 1608, F7, 3, 26) (dual of [(1608, 3), 4716, 27]-NRT-code) | [i] | ||