Information on Result #712476
Linear OA(751, 68, F7, 31) (dual of [68, 17, 32]-code), using construction XX applied to C1 = C([41,18]), C2 = C([0,23]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([41,23]) based on
- linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,18}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,23}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(78, 14, F7, 6) (dual of [14, 6, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 19, F7, 6) (dual of [19, 11, 7]-code), using
- linear OA(74, 6, F7, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,7)), using
- discarding factors / shortening the dual code based on linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
- Reed–Solomon code RS(3,7) [i]
- discarding factors / shortening the dual code based on linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), 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(750, 67, F7, 30) (dual of [67, 17, 31]-code) | [i] | Truncation | |
| 2 | Linear OOA(751, 34, F7, 2, 31) (dual of [(34, 2), 17, 32]-NRT-code) | [i] | OOA Folding | |