Information on Result #696634
Linear OA(3273, 1048600, F32, 18) (dual of [1048600, 1048527, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3249, 1048576, F32, 13) (dual of [1048576, 1048527, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), 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(3273, 1048600, F32, 2, 18) (dual of [(1048600, 2), 2097127, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (55, 73, 1048600)-net over F32 | [i] | ||
| 3 | Linear OOA(3273, 524300, F32, 2, 18) (dual of [(524300, 2), 1048527, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3273, 116511, F32, 18, 18) (dual of [(116511, 18), 2097125, 19]-NRT-code) | [i] | OA Folding and Stacking | |