Information on Result #712501
Linear OA(758, 69, F7, 39) (dual of [69, 11, 40]-code), using construction XX applied to C1 = C([7,39]), C2 = C([1,31]), C3 = C1 + C2 = C([7,31]), and C∩ = C1 ∩ C2 = C([1,39]) based on
- linear OA(742, 48, F7, 33) (dual of [48, 6, 34]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {7,8,…,39}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {7,8,…,31}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(79, 14, F7, 7) (dual of [14, 5, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- linear OA(75, 7, F7, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,7)), using
- Reed–Solomon code RS(2,7) [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, 23, F7, 3, 39) (dual of [(23, 3), 11, 40]-NRT-code) | [i] | OOA Folding | |