Information on Result #669042
Linear OA(4917, 2453, F49, 7) (dual of [2453, 2436, 8]-code), using generalized (u, u+v)-construction based on
- linear OA(490, 50, F49, 0) (dual of [50, 50, 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
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(490, 50, F49, 0) (dual of [50, 50, 1]-code) (see above)
- linear OA(491, 50, F49, 1) (dual of [50, 49, 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
- linear OA(491, 50, F49, 1) (dual of [50, 49, 2]-code) (see above)
- linear OA(491, 50, F49, 1) (dual of [50, 49, 2]-code) (see above)
- linear OA(491, 50, F49, 1) (dual of [50, 49, 2]-code) (see above)
- 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(493, 50, F49, 3) (dual of [50, 47, 4]-code or 50-arc in PG(2,49) or 50-cap in PG(2,49)), using
- extended Reed–Solomon code RSe(47,49) [i]
- oval in PG(2, 49) [i]
- algebraic-geometric code AG(F, Q+14P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(498, 53, F49, 7) (dual of [53, 45, 8]-code), using
- construction X applied to AG(F,21P) ⊂ AG(F,22P) [i] based on
- linear OA(497, 50, F49, 7) (dual of [50, 43, 8]-code or 50-arc in PG(6,49)), using algebraic-geometric code AG(F,21P) with degPÂ =Â 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
- linear OA(495, 50, F49, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using 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 (see above)
- linear OA(491, 3, F49, 1) (dual of [3, 2, 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 (see above)
- construction X applied to AG(F,21P) ⊂ AG(F,22P) [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
None.