MinT - Information on Result #2694556

Information on Result #2694556

Linear OOA(5²⁰, 125, F₅, 3, 7) (dual of [(125, 3), 355, 8]-NRT-code), using 5¹ times duplication based on linear OOA(5¹⁹, 125, F₅, 3, 7) (dual of [(125, 3), 356, 8]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
    - appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code) (see above)
3. linear OOA(5³, 25, F₅, 3, 2) (dual of [(25, 3), 72, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5³, 31, F₅, 3, 2) (dual of [(31, 3), 90, 3]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
4. linear OOA(5⁴, 25, F₅, 3, 3) (dual of [(25, 3), 71, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
    - ovoid in PG(3,Â 5) [i]
5. linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, 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.