Information on Result #696633
Linear OA(3277, 1048600, F32, 19) (dual of [1048600, 1048523, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3253, 1048576, F32, 14) (dual of [1048576, 1048523, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(3277, 1048600, F32, 2, 19) (dual of [(1048600, 2), 2097123, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (58, 77, 1048600)-net over F32 | [i] | ||
| 3 | Linear OOA(3277, 524300, F32, 2, 19) (dual of [(524300, 2), 1048523, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3277, 116511, F32, 19, 19) (dual of [(116511, 19), 2213632, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |