Information on Result #712479
Linear OA(758, 75, F7, 34) (dual of [75, 17, 35]-code), using construction XX applied to C1 = C([6,33]), C2 = C([0,24]), C3 = C1 + C2 = C([6,24]), and C∩ = C1 ∩ C2 = C([0,33]) based on
- linear OA(740, 48, F7, 28) (dual of [48, 8, 29]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,33}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(743, 48, F7, 34) (dual of [48, 5, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,24}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(710, 19, F7, 8) (dual of [19, 9, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- 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(758, 25, F7, 3, 34) (dual of [(25, 3), 17, 35]-NRT-code) | [i] | OOA Folding | |