Information on Result #685915
Linear OA(743, 57, F7, 29) (dual of [57, 14, 30]-code), using construction XX applied to C([1,63]) ⊂ C([1,51]) ⊂ C([1,49]) based on
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(787, 96, F7, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using contraction [i] based on linear OA(783, 96, F7, 51) (dual of [96, 13, 52]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(73, 8, F7, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,7) or 8-cap in PG(2,7)), using
- extended Reed–Solomon code RSe(5,7) [i]
- oval in PG(2, 7) [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(743, 19, F7, 3, 29) (dual of [(19, 3), 14, 30]-NRT-code) | [i] | OOA Folding | |