MinT - Information on Result #672005

Information on Result #672005

Linear OA(64¹⁶, 270209, F₆₄, 5) (dual of [270209, 270193, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64⁰, 4161, F₆₄, 0) (dual of [4161, 4161, 1]-code) (see above)
linear OA(64¹, 4161, F₆₄, 1) (dual of [4161, 4160, 2]-code), using
- discarding factors / shortening the dual code 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 OA(64¹, 4161, F₆₄, 1) (dual of [4161, 4160, 2]-code) (see above)
linear OA(64¹, 4161, F₆₄, 1) (dual of [4161, 4160, 2]-code) (see above)
linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
- Hamming code H(3,64) [i]
linear OA(64¹⁰, 8066, F₆₄, 5) (dual of [8066, 8056, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(64³, 4033, F₆₄, 2) (dual of [4033, 4030, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code) (see above)
  2. 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(64¹⁶, 135104, F₆₄, 2, 5) (dual of [(135104, 2), 270192, 6]-NRT-code)	[i]		OOA Folding