Information on Result #712460
Linear OA(741, 67, F7, 22) (dual of [67, 26, 23]-code), using construction XX applied to C1 = C([6,23]), C2 = C([1,17]), C3 = C1 + C2 = C([6,17]), 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(726, 48, F7, 17) (dual of [48, 22, 18]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(720, 48, F7, 12) (dual of [48, 28, 13]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,17}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(75, 11, F7, 4) (dual of [11, 6, 5]-code), using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using 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(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8 (see above)
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
- 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(741, 22, F7, 3, 22) (dual of [(22, 3), 25, 23]-NRT-code) | [i] | OOA Folding | |