Information on Result #689014
Linear OA(993, 4782984, F9, 15) (dual of [4782984, 4782891, 16]-code), using construction X applied to Ce(14) ⊂ Ce(12) based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(993, 4012511, F9, 2, 15) (dual of [(4012511, 2), 8024929, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(993, 4012511, F9, 3, 15) (dual of [(4012511, 3), 12037440, 16]-NRT-code) | [i] | ||
| 3 | Digital (78, 93, 4012511)-net over F9 | [i] | ||
| 4 | Linear OOA(993, 2391492, F9, 2, 15) (dual of [(2391492, 2), 4782891, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(993, 1594328, F9, 3, 15) (dual of [(1594328, 3), 4782891, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(993, 683283, F9, 15, 15) (dual of [(683283, 15), 10249152, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |