MinT - Information on Result #944751

Information on Result #944751

Linear OOA(9²², 58328, F₉, 3, 5) (dual of [(58328, 3), 174962, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(9²², 58329, F₉, 2, 5) (dual of [(58329, 2), 116636, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(9⁰, 6481, F₉, 2, 0) (dual of [(6481, 2), 12962, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁰, s, F₉, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(9⁰, 6481, F₉, 2, 0) (dual of [(6481, 2), 12962, 1]-NRT-code) (see above)
3. linear OOA(9⁰, 6481, F₉, 2, 0) (dual of [(6481, 2), 12962, 1]-NRT-code) (see above)
4. linear OOA(9⁰, 6481, F₉, 2, 0) (dual of [(6481, 2), 12962, 1]-NRT-code) (see above)
5. linear OOA(9¹, 6481, F₉, 2, 1) (dual of [(6481, 2), 12961, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
6. linear OOA(9¹, 6481, F₉, 2, 1) (dual of [(6481, 2), 12961, 2]-NRT-code) (see above)
7. linear OOA(9¹, 6481, F₉, 2, 1) (dual of [(6481, 2), 12961, 2]-NRT-code) (see above)
8. linear OOA(9⁵, 6481, F₉, 2, 2) (dual of [(6481, 2), 12957, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁵, 7381, F₉, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(9⁵, 7381, F₉, 2) (dual of [7381, 7376, 3]-code), using
      - Hamming code H(5,9) [i]
9. linear OOA(9¹⁴, 6481, F₉, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
    - trace code [i] 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		This result only	Method
1	Linear OOA(9⁹⁶, 5650730, F₉, 3, 10) (dual of [(5650730, 3), 16952094, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(9¹⁰⁴, 5650730, F₉, 3, 11) (dual of [(5650730, 3), 16952086, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs