Information on Result #682674
Linear OA(558, 15640, F5, 12) (dual of [15640, 15582, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(558, 10909, F5, 2, 12) (dual of [(10909, 2), 21760, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(558, 10909, F5, 3, 12) (dual of [(10909, 3), 32669, 13]-NRT-code) | [i] | ||
| 3 | Digital (46, 58, 10909)-net over F5 | [i] | ||
| 4 | Linear OOA(558, 7820, F5, 2, 12) (dual of [(7820, 2), 15582, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(558, 5213, F5, 3, 12) (dual of [(5213, 3), 15581, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(558, 2606, F5, 12, 12) (dual of [(2606, 12), 31214, 13]-NRT-code) | [i] | OA Folding and Stacking | |