Information on Result #686054
Linear OA(714, 50, F7, 9) (dual of [50, 36, 10]-code), using construction X applied to Ce(8) ⊂ Ce(7) based on
- linear OA(714, 49, F7, 9) (dual of [49, 35, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-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 OA(715, 51, F7, 9) (dual of [51, 36, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(795, 16862, F7, 19) (dual of [16862, 16767, 20]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(796, 16869, F7, 19) (dual of [16869, 16773, 20]-code) | [i] | ||
| 4 | Linear OA(790, 16862, F7, 18) (dual of [16862, 16772, 19]-code) | [i] | ||
| 5 | Linear OA(7105, 16858, F7, 21) (dual of [16858, 16753, 22]-code) | [i] | Construction X with Cyclic Codes | |
| 6 | Linear OA(7110, 16857, F7, 23) (dual of [16857, 16747, 24]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 7 | Linear OA(7105, 16857, F7, 22) (dual of [16857, 16752, 23]-code) | [i] | ||
| 8 | Linear OOA(714, 25, F7, 2, 9) (dual of [(25, 2), 36, 10]-NRT-code) | [i] | OOA Folding | |