Information on Result #686071
Linear OA(715, 55, F7, 8) (dual of [55, 40, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) 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(79, 49, F7, 5) (dual of [49, 40, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(72, 6, F7, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,7)), using
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- discarding factors / shortening the dual code based on linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), 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(7106, 16862, F7, 21) (dual of [16862, 16756, 22]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(7101, 16862, F7, 20) (dual of [16862, 16761, 21]-code) | [i] | ||
| 3 | Linear OOA(715, 27, F7, 2, 8) (dual of [(27, 2), 39, 9]-NRT-code) | [i] | OOA Folding | |