MinT - Information on Result #671991

Information on Result #671991

Linear OA(49¹⁵, 117747, F₄₉, 5) (dual of [117747, 117732, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 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
  - OA with only one run / dual of code without redundancy [i]
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 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
  - parity-check code [i]
linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 2]-code) (see above)
linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 2]-code) (see above)
linear OA(49³, 2403, F₄₉, 2) (dual of [2403, 2400, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(49³, 2451, F₄₉, 2) (dual of [2451, 2448, 3]-code), using
  - Hamming code H(3,49) [i]
linear OA(49⁹, 2403, F₄₉, 5) (dual of [2403, 2394, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(49², 50, F₄₉, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
    - extended Reedâ€“Solomon code RS_e(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]
  2. linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
    - a code by Danev and Olsson [i]

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		Method
1	Linear OOA(49¹⁵, 117747, F₄₉, 2, 5) (dual of [(117747, 2), 235479, 6]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(49¹⁵, 117747, F₄₉, 3, 5) (dual of [(117747, 3), 353226, 6]-NRT-code)	[i]
3	Digital (10, 15, 117747)-net over F₄₉	[i]
4	Linear OOA(49¹⁵, 58873, F₄₉, 2, 5) (dual of [(58873, 2), 117731, 6]-NRT-code)	[i]	OOA Folding