Information on Result #988678
Linear OOA(4947, 1921620, F49, 3, 11) (dual of [(1921620, 3), 5764813, 12]-NRT-code), using OOA 3-folding based on linear OA(4947, 5764860, F49, 11) (dual of [5764860, 5764813, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4947, 5764861, F49, 11) (dual of [5764861, 5764814, 12]-code), using
- (u, u+v)-construction [i] based on
- linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using
- extended Reed–Solomon code RSe(45,49) [i]
- the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,22P) with 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+14P) with degQ = 2 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 = 4 and degPÂ =Â 5 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(4942, 5764811, F49, 11) (dual of [5764811, 5764769, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(4941, 5764802, F49, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(4933, 5764802, F49, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using
- (u, u+v)-construction [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(794, 3843240, F7, 3, 11) (dual of [(3843240, 3), 11529626, 12]-NRT-code) | [i] | Trace Code for OOAs | |