MinT - Information on Result #907038

Information on Result #907038

Linear OOA(81¹⁵, 269082, F₈₁, 2, 5) (dual of [(269082, 2), 538149, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
linear OOA(81³, 3322, F₈₁, 2, 2) (dual of [(3322, 2), 6641, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
    - Hamming code H(3,81) [i]
linear OOA(81⁹, 3322, F₈₁, 2, 5) (dual of [(3322, 2), 6635, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
  2. linear OOA(81⁷, 3240, F₈₁, 2, 5) (dual of [(3240, 2), 6473, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁷, 6480, F₈₁, 5) (dual of [6480, 6473, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 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(81⁵⁶, 4463383, F₈₁, 2, 11) (dual of [(4463383, 2), 8926710, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁵², 4463383, F₈₁, 2, 10) (dual of [(4463383, 2), 8926714, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(81¹⁵, 269081, F₈₁, 3, 5) (dual of [(269081, 3), 807228, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(81¹⁵, 269081, F₈₁, 4, 5) (dual of [(269081, 4), 1076309, 6]-NRT-code)	[i]	OOA Stacking with Additional Row