MinT - Information on Result #906687

Information on Result #906687

Linear OOA(9²⁴, 58419, F₉, 2, 5) (dual of [(58419, 2), 116814, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 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]
linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 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]
linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
linear OOA(9⁵, 6491, F₉, 2, 2) (dual of [(6491, 2), 12977, 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]
linear OOA(9¹⁶, 6491, F₉, 2, 5) (dual of [(6491, 2), 12966, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9², 10, F₉, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;18,9) [i]
  2. 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(9²⁴, 58418, F₉, 3, 5) (dual of [(58418, 3), 175230, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(9²⁴, 58418, F₉, 6, 5) (dual of [(58418, 6), 350484, 6]-NRT-code)	[i]		OOA Stacking with Additional Row