Information on Result #712437
Linear OA(745, 74, F7, 23) (dual of [74, 29, 24]-code), using construction XX applied to C1 = C([6,23]), C2 = C([1,15]), C3 = C1 + C2 = C([6,15]), and C∩ = C1 ∩ C2 = C([1,23]) based on
- linear OA(728, 48, F7, 18) (dual of [48, 20, 19]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,23}, and designed minimum distance d ≥ |I|+1 = 19 [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(732, 48, F7, 23) (dual of [48, 16, 24]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 24 [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(79, 18, F7, 7) (dual of [18, 9, 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(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(745, 37, F7, 2, 23) (dual of [(37, 2), 29, 24]-NRT-code) | [i] | OOA Folding | |