Information on Result #2283739
Linear OA(969, 531456, F9, 13) (dual of [531456, 531387, 14]-code), using 1 times code embedding in larger space based on linear OA(968, 531455, F9, 13) (dual of [531455, 531387, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- 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(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(913, 14, F9, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,9)), using
- dual of repetition code with length 14 [i]
- linear OA(91, 14, F9, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-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 OOA(969, 486265, F9, 2, 13) (dual of [(486265, 2), 972461, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(969, 486265, F9, 3, 13) (dual of [(486265, 3), 1458726, 14]-NRT-code) | [i] | ||
| 3 | Digital (56, 69, 486265)-net over F9 | [i] | ||
| 4 | Linear OOA(969, 265728, F9, 2, 13) (dual of [(265728, 2), 531387, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(969, 177152, F9, 3, 13) (dual of [(177152, 3), 531387, 14]-NRT-code) | [i] | ||