Information on Result #684585
Linear OA(7104, 823597, F7, 16) (dual of [823597, 823493, 17]-code), using construction X applied to Ce(15) ⊂ Ce(8) based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(750, 823543, F7, 9) (dual of [823543, 823493, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(712, 54, F7, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(712, 100, F7, 6) (dual of [100, 88, 7]-code), using
- trace code [i] based on linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using
- extended Reed–Solomon code RSe(44,49) [i]
- algebraic-geometric code AG(F, Q+20P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
- algebraic-geometric code AG(F, Q+13P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- trace code [i] based on linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using
- discarding factors / shortening the dual code based on linear OA(712, 100, F7, 6) (dual of [100, 88, 7]-code), using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7104, 823597, F7, 2, 16) (dual of [(823597, 2), 1647090, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7104, 823597, F7, 3, 16) (dual of [(823597, 3), 2470687, 17]-NRT-code) | [i] | ||
| 3 | Digital (88, 104, 823597)-net over F7 | [i] | ||
| 4 | Linear OOA(7104, 411798, F7, 2, 16) (dual of [(411798, 2), 823492, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7104, 274532, F7, 3, 16) (dual of [(274532, 3), 823492, 17]-NRT-code) | [i] | ||