Information on Result #682986
Linear OA(516, 3130, F5, 4) (dual of [3130, 3114, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(516, 3125, F5, 4) (dual of [3125, 3109, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(511, 3125, F5, 3) (dual of [3125, 3114, 4]-code or 3125-cap in PG(10,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(516, 3130, F5, 2, 4) (dual of [(3130, 2), 6244, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(516, 3130, F5, 3, 4) (dual of [(3130, 3), 9374, 5]-NRT-code) | [i] | ||
| 3 | Linear OA(517, 4447, F5, 4) (dual of [4447, 4430, 5]-code) | [i] | Varšamov–Edel Lengthening | |
| 4 | Linear OA(518, 7206, F5, 4) (dual of [7206, 7188, 5]-code) | [i] | ||
| 5 | Linear OOA(516, 1565, F5, 2, 4) (dual of [(1565, 2), 3114, 5]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(516, 1565, F5, 3, 4) (dual of [(1565, 3), 4679, 5]-NRT-code) | [i] | OA Folding and Stacking | |