MinT - Information on Result #906904

Information on Result #906904

Linear OOA(49¹⁵, 60074, F₄₉, 2, 5) (dual of [(60074, 2), 120133, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
linear OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] 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 OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code) (see above)
linear OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code) (see above)
linear OOA(49³, 1226, F₄₉, 2, 2) (dual of [(1226, 2), 2449, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49³, 2451, F₄₉, 2, 2) (dual of [(2451, 2), 4899, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(49³, 2451, F₄₉, 2) (dual of [2451, 2448, 3]-code), using
    - Hamming code H(3,49) [i]
linear OOA(49⁹, 1226, F₄₉, 2, 5) (dual of [(1226, 2), 2443, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49², 50, F₄₉, 2, 2) (dual of [(50, 2), 98, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;98,49) [i]
  2. linear OOA(49⁷, 1176, F₄₉, 2, 5) (dual of [(1176, 2), 2345, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(49⁷, 2352, F₄₉, 5) (dual of [2352, 2345, 6]-code), using
      - discarding factors / shortening the dual code based on 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		This result only	Method
1	Linear OOA(49¹⁵, 60073, F₄₉, 3, 5) (dual of [(60073, 3), 180204, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(49¹⁵, 60073, F₄₉, 6, 5) (dual of [(60073, 6), 360423, 6]-NRT-code)	[i]		OOA Stacking with Additional Row