MinT - Information on Result #906613

Information on Result #906613

Linear OOA(7²², 250, F₇, 2, 7) (dual of [(250, 2), 478, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7¹, 50, F₇, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹, s, F₇, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(7¹, 50, F₇, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code) (see above)
linear OOA(7³, 50, F₇, 2, 2) (dual of [(50, 2), 97, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7³, 57, F₇, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(7³, 57, F₇, 2) (dual of [57, 54, 3]-code), using
    - Hamming code H(3,7) [i]
linear OOA(7⁴, 50, F₇, 2, 3) (dual of [(50, 2), 96, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁴, 50, F₇, 3) (dual of [50, 46, 4]-code or 50-cap in PG(3,7)), using
  - ovoid in PG(3,Â 7) [i]
linear OOA(7¹³, 50, F₇, 2, 7) (dual of [(50, 2), 87, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 50)-net over F₇, using
  - base reduction for projective spaces (embedding PG(6,49) in PG(12,7)) for nets [i] based on digital (0, 7, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [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.