Information on Result #689009
Linear OA(9114, 4782984, F9, 18) (dual of [4782984, 4782870, 19]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(9114, 4664291, F9, 2, 18) (dual of [(4664291, 2), 9328468, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9114, 4664291, F9, 3, 18) (dual of [(4664291, 3), 13992759, 19]-NRT-code) | [i] | ||
| 3 | Digital (96, 114, 4664291)-net over F9 | [i] | ||
| 4 | Linear OOA(9114, 2391492, F9, 2, 18) (dual of [(2391492, 2), 4782870, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9114, 1594328, F9, 3, 18) (dual of [(1594328, 3), 4782870, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(9114, 531442, F9, 18, 18) (dual of [(531442, 18), 9565842, 19]-NRT-code) | [i] | OA Folding and Stacking | |