Information on Result #685820
Linear OA(746, 56, F7, 33) (dual of [56, 10, 34]-code), using construction X applied to C([0,65]) ⊂ C([0,53]) based on
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using contraction [i] based on linear OA(789, 96, F7, 67) (dual of [96, 7, 68]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,65], and minimum distance d ≥ |{−1,0,…,65}|+1 = 68 (BCH-bound) [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using contraction [i] based on linear OA(786, 96, F7, 55) (dual of [96, 10, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,53], and minimum distance d ≥ |{−1,0,…,53}|+1 = 56 (BCH-bound) [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
- extended Reed–Solomon code RSe(3,7) [i]
- the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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.
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(746, 28, F7, 2, 33) (dual of [(28, 2), 10, 34]-NRT-code) | [i] | OOA Folding | |