Information on Result #712455
Linear OA(748, 75, F7, 25) (dual of [75, 27, 26]-code), using construction XX applied to C1 = C([5,24]), C2 = C([0,15]), C3 = C1 + C2 = C([5,15]), and C∩ = C1 ∩ C2 = C([0,24]) based on
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {5,6,…,24}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(724, 48, F7, 16) (dual of [48, 24, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 17 [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(719, 48, F7, 11) (dual of [48, 29, 12]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {5,6,…,15}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 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]
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(748, 37, F7, 2, 25) (dual of [(37, 2), 26, 26]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(748, 25, F7, 3, 25) (dual of [(25, 3), 27, 26]-NRT-code) | [i] | ||