Information on Result #689710
Linear OA(971, 6571, F9, 20) (dual of [6571, 6500, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) based on
- linear OA(969, 6561, F9, 20) (dual of [6561, 6492, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(961, 6561, F9, 17) (dual of [6561, 6500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
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(972, 6572, F9, 20) (dual of [6572, 6500, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(971, 4843, F9, 2, 20) (dual of [(4843, 2), 9615, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(971, 4843, F9, 3, 20) (dual of [(4843, 3), 14458, 21]-NRT-code) | [i] | ||
| 4 | Digital (51, 71, 4843)-net over F9 | [i] | ||
| 5 | Linear OOA(971, 3285, F9, 2, 20) (dual of [(3285, 2), 6499, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(971, 2190, F9, 3, 20) (dual of [(2190, 3), 6499, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(971, 657, F9, 20, 20) (dual of [(657, 20), 13069, 21]-NRT-code) | [i] | OA Folding and Stacking | |