MinT - Information on Result #971916

Information on Result #971916

Linear OOA(5¹⁸, 50, F₅, 3, 7) (dual of [(50, 3), 132, 8]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁸, 100, F₅, 2, 7) (dual of [(100, 2), 182, 8]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5¹, 25, F₅, 2, 1) (dual of [(25, 2), 49, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [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(5³, 25, F₅, 2, 2) (dual of [(25, 2), 47, 3]-NRT-code), using
  - discarding factors / shortening the dual code 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]
3. linear OOA(5⁴, 25, F₅, 2, 3) (dual of [(25, 2), 46, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁴, 26, F₅, 2, 3) (dual of [(26, 2), 48, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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]
4. linear OOA(5¹⁰, 25, F₅, 2, 7) (dual of [(25, 2), 40, 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.