Information on Result #685962
Linear OA(721, 28, F7, 15) (dual of [28, 7, 16]-code), using construction X applied to C([1,47]) ⊂ C([1,38]) based on
- linear OA(719, 24, F7, 15) (dual of [24, 5, 16]-code), using contraction [i] based on linear OA(767, 72, F7, 47) (dual of [72, 5, 48]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(717, 24, F7, 12) (dual of [24, 7, 13]-code), using contraction [i] based on linear OA(765, 72, F7, 38) (dual of [72, 7, 39]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(72, 4, F7, 2) (dual of [4, 2, 3]-code or 4-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(777, 84, F7, 56) (dual of [84, 7, 57]-code) | [i] | Construction X with Cyclic Codes | |