MinT - Information on Result #944558

Information on Result #944558

Linear OOA(5²², 3004, F₅, 3, 5) (dual of [(3004, 3), 8990, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(5²², 3005, F₅, 2, 5) (dual of [(3005, 2), 5988, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code) (see above)
3. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code) (see above)
4. linear OOA(5⁵, 601, F₅, 2, 2) (dual of [(601, 2), 1197, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁵, 781, F₅, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(5⁵, 781, F₅, 2) (dual of [781, 776, 3]-code), using
      - Hamming code H(5,5) [i]
5. linear OOA(5¹⁴, 601, F₅, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
    - trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 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(5¹¹⁴, 4197305, F₅, 3, 10) (dual of [(4197305, 3), 12591801, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs