MinT - Information on Result #961049

Information on Result #961049

Linear OOA(4¹⁹, 35, F₄, 3, 7) (dual of [(35, 3), 86, 8]-NRT-code), using OOA 2-folding based on linear OOA(4¹⁹, 70, F₄, 2, 7) (dual of [(70, 2), 121, 8]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁹, 71, F₄, 2, 7) (dual of [(71, 2), 123, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹, 17, F₄, 2, 1) (dual of [(17, 2), 33, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(4³, 17, F₄, 2, 2) (dual of [(17, 2), 31, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [i]
  3. linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
      - ovoid in PG(3,Â 4) [i]
  4. linear OOA(4¹¹, 20, F₄, 2, 7) (dual of [(20, 2), 29, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
      - linear code embedding found in a computer search [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

None.