Information on Result #696591
Linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1048576, F32, 2) (dual of [1048576, 1048571, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-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(3214, 1048586, F32, 2, 4) (dual of [(1048586, 2), 2097158, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (10, 14, 1048586)-net over F32 | [i] | ||
| 3 | Linear OOA(3214, 524293, F32, 2, 4) (dual of [(524293, 2), 1048572, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3214, 524293, F32, 4, 4) (dual of [(524293, 4), 2097158, 5]-NRT-code) | [i] | OA Folding and Stacking | |