Information on Result #712442
Linear OA(747, 76, F7, 24) (dual of [76, 29, 25]-code), using construction XX applied to C1 = C([6,24]), C2 = C([1,15]), C3 = C1 + C2 = C([6,15]), and C∩ = C1 ∩ C2 = C([1,24]) based on
- 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(723, 48, F7, 15) (dual of [48, 25, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(717, 48, F7, 10) (dual of [48, 31, 11]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,15}, and designed minimum distance d ≥ |I|+1 = 11 [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, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [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(747, 38, F7, 2, 24) (dual of [(38, 2), 29, 25]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(747, 25, F7, 3, 24) (dual of [(25, 3), 28, 25]-NRT-code) | [i] | ||