MinT - Information on Result #906309

Information on Result #906309

Linear OOA(4¹⁹, 71, F₄, 2, 7) (dual of [(71, 2), 123, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

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]
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]
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]
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: