MinT - Information on Result #1022160

Information on Result #1022160

Linear OOA(64¹⁵, 133184, F₆₄, 3, 5) (dual of [(133184, 3), 399537, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
linear OOA(64¹, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [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, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 2]-NRT-code) (see above)
linear OOA(64¹, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 2]-NRT-code) (see above)
linear OOA(64³, 2081, F₆₄, 3, 2) (dual of [(2081, 3), 6240, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 3, 2) (dual of [(4161, 3), 12480, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
      - Hamming code H(3,64) [i]
linear OOA(64⁹, 2081, F₆₄, 3, 5) (dual of [(2081, 3), 6234, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
  2. linear OOA(64⁷, 2016, F₆₄, 3, 5) (dual of [(2016, 3), 6041, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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(64⁵⁶, 2929385, F₆₄, 3, 11) (dual of [(2929385, 3), 8788099, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵², 2929385, F₆₄, 3, 10) (dual of [(2929385, 3), 8788103, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs