Information on Result #734652
Linear OA(4929, 117702, F49, 9) (dual of [117702, 117673, 10]-code), using (u, u+v)-construction based on
- linear OA(494, 50, F49, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using
- extended Reed–Solomon code RSe(46,49) [i]
- algebraic-geometric code AG(F, Q+21P) 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,15P) with degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(4925, 117652, F49, 9) (dual of [117652, 117627, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(4925, 117649, F49, 9) (dual of [117649, 117624, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
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(4929, 117702, F49, 2, 9) (dual of [(117702, 2), 235375, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4929, 117702, F49, 3, 9) (dual of [(117702, 3), 353077, 10]-NRT-code) | [i] | ||
| 3 | Digital (20, 29, 117702)-net over F49 | [i] | ||
| 4 | Linear OOA(4929, 58851, F49, 2, 9) (dual of [(58851, 2), 117673, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4929, 39234, F49, 3, 9) (dual of [(39234, 3), 117673, 10]-NRT-code) | [i] | ||