MinT - Information on Result #906981

Information on Result #906981

Linear OOA(64⁹, 4175, F₆₄, 2, 4) (dual of [(4175, 2), 8341, 5]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
linear OOA(64⁵, 80, F₆₄, 2, 4) (dual of [(80, 2), 155, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,155P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
  - a function field by SÃ©mirat [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(64⁴², 4198476, F₆₄, 2, 9) (dual of [(4198476, 2), 8396910, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(64³⁸, 4198476, F₆₄, 2, 8) (dual of [(4198476, 2), 8396914, 9]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(64⁹, 4174, F₆₄, 3, 4) (dual of [(4174, 3), 12513, 5]-NRT-code)	[i]	OOA Stacking with Additional Row