Information on Result #731027
Linear OA(740, 235316, F7, 7) (dual of [235316, 235276, 8]-code), using trace code based on linear OA(4920, 117658, F49, 7) (dual of [117658, 117638, 8]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(4919, 117650, F49, 7) (dual of [117650, 117631, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(4913, 117650, F49, 5) (dual of [117650, 117637, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(497, 8, F49, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,49)), using
- dual of repetition code with length 8 [i]
- linear OA(491, 8, F49, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(741, 235317, F7, 7) (dual of [235317, 235276, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(740, 235316, F7, 2, 7) (dual of [(235316, 2), 470592, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(740, 235316, F7, 3, 7) (dual of [(235316, 3), 705908, 8]-NRT-code) | [i] | ||
| 4 | Digital (33, 40, 235316)-net over F7 | [i] | ||
| 5 | Linear OOA(740, 117658, F7, 2, 7) (dual of [(117658, 2), 235276, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(740, 78438, F7, 3, 7) (dual of [(78438, 3), 235274, 8]-NRT-code) | [i] | ||
| 7 | Linear OOA(740, 78438, F7, 7, 7) (dual of [(78438, 7), 549026, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |