Information on Result #2284172
Linear OA(9130, 4782987, F9, 21) (dual of [4782987, 4782857, 22]-code), using 2 times code embedding in larger space based on linear OA(9128, 4782985, F9, 21) (dual of [4782985, 4782857, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(9127, 4782970, F9, 21) (dual of [4782970, 4782843, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [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(9130, 2984890, F9, 2, 21) (dual of [(2984890, 2), 5969650, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9130, 2984890, F9, 3, 21) (dual of [(2984890, 3), 8954540, 22]-NRT-code) | [i] | ||
| 3 | Digital (109, 130, 2984890)-net over F9 | [i] | ||
| 4 | Linear OOA(9130, 1594329, F9, 3, 21) (dual of [(1594329, 3), 4782857, 22]-NRT-code) | [i] | OOA Folding | |