Information on Result #684583
Linear OA(7110, 823593, F7, 17) (dual of [823593, 823483, 18]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
- linear OA(799, 823543, F7, 17) (dual of [823543, 823444, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(711, 50, F7, 6) (dual of [50, 39, 7]-code), using
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [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)
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), 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(7110, 274531, F7, 3, 17) (dual of [(274531, 3), 823483, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7110, 102949, F7, 17, 17) (dual of [(102949, 17), 1750023, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |