Information on Result #689020
Linear OA(972, 4782984, F9, 12) (dual of [4782984, 4782912, 13]-code), using construction X applied to Ce(11) ⊂ Ce(9) based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-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(972, 3372931, F9, 2, 12) (dual of [(3372931, 2), 6745790, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(972, 3372931, F9, 3, 12) (dual of [(3372931, 3), 10118721, 13]-NRT-code) | [i] | ||
| 3 | Digital (60, 72, 3372931)-net over F9 | [i] | ||
| 4 | Linear OOA(972, 2391492, F9, 2, 12) (dual of [(2391492, 2), 4782912, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(972, 1594328, F9, 3, 12) (dual of [(1594328, 3), 4782912, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(972, 797164, F9, 12, 12) (dual of [(797164, 12), 9565896, 13]-NRT-code) | [i] | OA Folding and Stacking | |