Information on Result #689419
Linear OA(959, 59067, F9, 13) (dual of [59067, 59008, 14]-code), using construction X applied to Ce(12) ⊂ Ce(9) based on
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-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(960, 59068, F9, 13) (dual of [59068, 59008, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(959, 59067, F9, 2, 13) (dual of [(59067, 2), 118075, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(959, 59067, F9, 3, 13) (dual of [(59067, 3), 177142, 14]-NRT-code) | [i] | ||
| 4 | Digital (46, 59, 59067)-net over F9 | [i] | ||
| 5 | Linear OA(960, 59069, F9, 13) (dual of [59069, 59009, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(961, 59071, F9, 13) (dual of [59071, 59010, 14]-code) | [i] | ||
| 7 | Linear OOA(959, 29533, F9, 2, 13) (dual of [(29533, 2), 59007, 14]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(959, 19689, F9, 3, 13) (dual of [(19689, 3), 59008, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(959, 9844, F9, 13, 13) (dual of [(9844, 13), 127913, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |