MinT - Information on Result #944695

Information on Result #944695

Linear OOA(8²⁴, 32335, F₈, 3, 5) (dual of [(32335, 3), 96981, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(8²⁴, 32336, F₈, 2, 5) (dual of [(32336, 2), 64648, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁰, s, F₈, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
3. linear OOA(8⁰, 4042, F₈, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
4. linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [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]
5. linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
6. linear OOA(8¹, 4042, F₈, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
7. linear OOA(8⁵, 4042, F₈, 2, 2) (dual of [(4042, 2), 8079, 3]-NRT-code), using
  - discarding factors / shortening the dual code 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]
8. linear OOA(8¹⁶, 4042, F₈, 2, 5) (dual of [(4042, 2), 8068, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8², 9, F₈, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;16,8) [i]
    2. linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
      - OOA 2-folding [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(8⁹⁸, 5624737, F₈, 3, 10) (dual of [(5624737, 3), 16874113, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹⁰⁶, 5624737, F₈, 3, 11) (dual of [(5624737, 3), 16874105, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs