MinT - Information on Result #906310

Information on Result #906310

Linear OOA(4²⁰, 80, F₄, 2, 7) (dual of [(80, 2), 140, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4¹, 20, F₄, 2, 1) (dual of [(20, 2), 39, 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]
linear OOA(4³, 20, F₄, 2, 2) (dual of [(20, 2), 37, 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]
linear OOA(4⁵, 20, F₄, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
    - a cap found by Tallinii [i]
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.

None.

The following results depend on this result: