Information on Result #893927
Linear OOA(730, 5764854, F7, 2, 4) (dual of [(5764854, 2), 11529678, 5]-NRT-code), using trace code based on linear OOA(4915, 2882427, F49, 2, 4) (dual of [(2882427, 2), 5764839, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4915, 5764854, F49, 4) (dual of [5764854, 5764839, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4915, 5764855, F49, 4) (dual of [5764855, 5764840, 5]-code), using
- (u, u+v)-construction [i] based on
- linear OA(492, 50, F49, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
- extended Reed–Solomon code RSe(48,49) [i]
- Hamming code H(2,49) [i]
- algebraic-geometric code AG(F, Q+22P) 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]
- linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 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(3) ⊂ Ce(2) [i] based on
- linear OA(492, 50, F49, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4915, 5764855, F49, 4) (dual of [5764855, 5764840, 5]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.