Information on Result #689393
Linear OA(927, 59061, F9, 6) (dual of [59061, 59034, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(926, 59049, F9, 6) (dual of [59049, 59023, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(916, 59049, F9, 4) (dual of [59049, 59033, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(911, 12, F9, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,9)), using
- dual of repetition code with length 12 [i]
- linear OA(91, 12, F9, 1) (dual of [12, 11, 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 OA(928, 59062, F9, 6) (dual of [59062, 59034, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(927, 59061, F9, 2, 6) (dual of [(59061, 2), 118095, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(927, 59061, F9, 3, 6) (dual of [(59061, 3), 177156, 7]-NRT-code) | [i] | ||
| 4 | Digital (21, 27, 59061)-net over F9 | [i] | ||
| 5 | Linear OOA(927, 19687, F9, 3, 6) (dual of [(19687, 3), 59034, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(927, 19687, F9, 6, 6) (dual of [(19687, 6), 118095, 7]-NRT-code) | [i] | OA Folding and Stacking | |