Information on Result #712483
Linear OA(747, 64, F7, 29) (dual of [64, 17, 30]-code), using construction XX applied to C1 = C([7,31]), C2 = C([1,25]), C3 = C1 + C2 = C([7,25]), and C∩ = C1 ∩ C2 = C([1,31]) based on
- 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(735, 48, F7, 25) (dual of [48, 13, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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 = {7,8,…,25}, and designed minimum distance d ≥ |I|+1 = 20 [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]
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)) (see above)
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, 32, F7, 2, 29) (dual of [(32, 2), 17, 30]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(747, 21, F7, 3, 29) (dual of [(21, 3), 16, 30]-NRT-code) | [i] | ||