Information on Result #657396

Linear OA(499, 53, F49, 8) (dual of [53, 44, 9]-code), using construction X applied to AG(F, Q+19P) ⊂ AG(F, Q+20P) based on
  1. linear OA(498, 50, F49, 8) (dual of [50, 42, 9]-code or 50-arc in PG(7,49)), using algebraic-geometric code AG(F, Q+19P) with degQ = 3 and degP = 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using the rational function field F49(x) [i]
  2. linear OA(496, 50, F49, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using algebraic-geometric code AG(F, Q+20P) with degQ = 3 and degP = 2 [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using

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:

ResultThis
result
only		Method
1Linear OA(4927, 106, F49, 17) (dual of [106, 79, 18]-code) [i](u, u+v)-Construction
2Linear OA(4928, 108, F49, 17) (dual of [108, 80, 18]-code) [i]
3Linear OA(4942, 2455, F49, 17) (dual of [2455, 2413, 18]-code) [i]
4Linear OA(4926, 106, F49, 16) (dual of [106, 80, 17]-code) [i]
5Linear OA(4940, 2454, F49, 16) (dual of [2454, 2414, 17]-code) [i]
6Linear OA(4955, 117702, F49, 16) (dual of [117702, 117647, 17]-code) [i]
7Linear OA(4942, 2456, F49, 17) (dual of [2456, 2414, 18]-code) [i]
8Linear OA(4943, 2460, F49, 17) (dual of [2460, 2417, 18]-code) [i]
9Linear OA(4940, 2456, F49, 16) (dual of [2456, 2416, 17]-code) [i]
10Linear OA(4941, 2459, F49, 16) (dual of [2459, 2418, 17]-code) [i]
11Linear OA(4942, 2462, F49, 16) (dual of [2462, 2420, 17]-code) [i]
12Linear OA(4955, 117705, F49, 16) (dual of [117705, 117650, 17]-code) [i]
13Linear OA(4947, 2505, F49, 17) (dual of [2505, 2458, 18]-code) [i](u, u−v, u+v+w)-Construction