Information on Result #869115
Linear OOA(3217, 513, F32, 2, 9) (dual of [(513, 2), 1009, 10]-NRT-code), using OOA 2-folding based on linear OA(3217, 1026, F32, 9) (dual of [1026, 1009, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(3217, 1024, F32, 9) (dual of [1024, 1007, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(3221, 546, F32, 2, 9) (dual of [(546, 2), 1071, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3222, 557, F32, 2, 9) (dual of [(557, 2), 1092, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(32103, 4194814, F32, 2, 18) (dual of [(4194814, 2), 8389525, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(32108, 4194814, F32, 2, 19) (dual of [(4194814, 2), 8389520, 20]-NRT-code) | [i] | ||
| 5 | OOA(32100, 4194814, S32, 2, 18) | [i] | ||
| 6 | OOA(32105, 4194814, S32, 2, 19) | [i] | ||
| 7 | Digital (8, 17, 513)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |