Information on Result #2284159
Linear OA(993, 59062, F9, 21) (dual of [59062, 58969, 22]-code), using 1 times code embedding in larger space based on linear OA(992, 59061, F9, 21) (dual of [59061, 58969, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(991, 59050, F9, 21) (dual of [59050, 58959, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(981, 59050, F9, 19) (dual of [59050, 58969, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 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, 41357, F9, 2, 21) (dual of [(41357, 2), 82621, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(993, 41357, F9, 3, 21) (dual of [(41357, 3), 123978, 22]-NRT-code) | [i] | ||
| 3 | Digital (72, 93, 41357)-net over F9 | [i] | ||
| 4 | Linear OOA(993, 29531, F9, 2, 21) (dual of [(29531, 2), 58969, 22]-NRT-code) | [i] | OOA Folding | |