Information on Result #689223
Linear OA(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), 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 OA(9105, 531479, F9, 19) (dual of [531479, 531374, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(9106, 531480, F9, 19) (dual of [531480, 531374, 20]-code) | [i] | ||
| 3 | Linear OA(9103, 531477, F9, 18) (dual of [531477, 531374, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(9104, 531478, F9, 2, 19) (dual of [(531478, 2), 1062852, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(9104, 531478, F9, 3, 19) (dual of [(531478, 3), 1594330, 20]-NRT-code) | [i] | ||
| 6 | Digital (85, 104, 531478)-net over F9 | [i] | ||
| 7 | Linear OA(9105, 531480, F9, 19) (dual of [531480, 531375, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(9106, 531482, F9, 19) (dual of [531482, 531376, 20]-code) | [i] | ||
| 9 | Linear OOA(9104, 265739, F9, 2, 19) (dual of [(265739, 2), 531374, 20]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(9104, 177159, F9, 3, 19) (dual of [(177159, 3), 531373, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(9104, 59053, F9, 19, 19) (dual of [(59053, 19), 1121903, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |