Information on Result #686055
Linear OA(714, 52, F7, 8) (dual of [52, 38, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(713, 49, F7, 8) (dual of [49, 36, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(711, 49, F7, 6) (dual of [49, 38, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(714, 32, F7, 2, 8) (dual of [(32, 2), 50, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(714, 32, F7, 3, 8) (dual of [(32, 3), 82, 9]-NRT-code) | [i] | ||
| 3 | Digital (6, 14, 32)-net over F7 | [i] | ||
| 4 | Linear OA(7105, 16859, F7, 21) (dual of [16859, 16754, 22]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 5 | Linear OA(7100, 16859, F7, 20) (dual of [16859, 16759, 21]-code) | [i] | ||
| 6 | Linear OOA(714, 26, F7, 2, 8) (dual of [(26, 2), 38, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(714, 17, F7, 3, 8) (dual of [(17, 3), 37, 9]-NRT-code) | [i] | ||