MinT - Information on Result #1021995

Information on Result #1021995

Linear OOA(8²³, 32264, F₈, 3, 5) (dual of [(32264, 3), 96769, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8⁰, 4033, F₈, 3, 0) (dual of [(4033, 3), 12099, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁰, s, F₈, 3, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(8⁰, 4033, F₈, 3, 0) (dual of [(4033, 3), 12099, 1]-NRT-code) (see above)
linear OOA(8⁰, 4033, F₈, 3, 0) (dual of [(4033, 3), 12099, 1]-NRT-code) (see above)
linear OOA(8¹, 4033, F₈, 3, 1) (dual of [(4033, 3), 12098, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(8¹, 4033, F₈, 3, 1) (dual of [(4033, 3), 12098, 2]-NRT-code) (see above)
linear OOA(8¹, 4033, F₈, 3, 1) (dual of [(4033, 3), 12098, 2]-NRT-code) (see above)
linear OOA(8⁵, 4033, F₈, 3, 2) (dual of [(4033, 3), 12094, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁵, 4681, F₈, 3, 2) (dual of [(4681, 3), 14038, 3]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(8⁵, 4681, F₈, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(8⁵, 4681, F₈, 2) (dual of [4681, 4676, 3]-code), using
      - Hamming code H(5,8) [i]
linear OOA(8¹⁵, 4033, F₈, 3, 5) (dual of [(4033, 3), 12084, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8¹⁵, 8067, F₈, 5) (dual of [8067, 8052, 6]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
    - trace code [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(8¹⁰⁵, 5624666, F₈, 3, 11) (dual of [(5624666, 3), 16873893, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8⁹⁷, 5624666, F₈, 3, 10) (dual of [(5624666, 3), 16873901, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs