Information on Result #682683
Linear OA(528, 15640, F5, 6) (dual of [15640, 15612, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 15625, F5, 3) (dual of [15625, 15612, 4]-code or 15625-cap in PG(12,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(53, 15, F5, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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(528, 15640, F5, 2, 6) (dual of [(15640, 2), 31252, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(528, 15640, F5, 3, 6) (dual of [(15640, 3), 46892, 7]-NRT-code) | [i] | ||
| 3 | Digital (22, 28, 15640)-net over F5 | [i] | ||
| 4 | Linear OOA(528, 7820, F5, 2, 6) (dual of [(7820, 2), 15612, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(528, 5213, F5, 3, 6) (dual of [(5213, 3), 15611, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(528, 5213, F5, 6, 6) (dual of [(5213, 6), 31250, 7]-NRT-code) | [i] | OA Folding and Stacking | |