MinT - Information on Result #906689

Information on Result #906689

Linear OOA(9²², 410, F₉, 2, 7) (dual of [(410, 2), 798, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(9¹, 82, F₉, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(9¹, 82, F₉, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
linear OOA(9³, 82, F₉, 2, 2) (dual of [(82, 2), 161, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³, 91, F₉, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(9³, 91, F₉, 2) (dual of [91, 88, 3]-code), using
    - Hamming code H(3,9) [i]
linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
  - ovoid in PG(3,Â 9) [i]
linear OOA(9¹³, 82, F₉, 2, 7) (dual of [(82, 2), 151, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 82)-net over F₉, using
  - base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) for nets [i] based on digital (0, 7, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(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.