Information on Result #696647
Linear OA(3274, 1048605, F32, 18) (dual of [1048605, 1048531, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) 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(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), 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(3274, 1048605, F32, 2, 18) (dual of [(1048605, 2), 2097136, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (56, 74, 1048605)-net over F32 | [i] | ||
| 3 | Linear OOA(3274, 524302, F32, 2, 18) (dual of [(524302, 2), 1048530, 19]-NRT-code) | [i] | OOA Folding | |