Information on Result #1008912
Linear OOA(7110, 3843236, F7, 3, 13) (dual of [(3843236, 3), 11529598, 14]-NRT-code), using trace code based on linear OOA(4955, 1921618, F49, 3, 13) (dual of [(1921618, 3), 5764799, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4955, 5764854, F49, 13) (dual of [5764854, 5764799, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4955, 5764855, F49, 13) (dual of [5764855, 5764800, 14]-code), using
- (u, u+v)-construction [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)
- linear OA(4949, 5764805, F49, 13) (dual of [5764805, 5764756, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4949, 5764801, F49, 13) (dual of [5764801, 5764752, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4955, 5764855, F49, 13) (dual of [5764855, 5764800, 14]-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.