MinT - Information on Result #975199

Information on Result #975199

Linear OOA(5¹⁵⁰, 68, F₅, 3, 72) (dual of [(68, 3), 54, 73]-NRT-code), using OOA 3-folding based on linear OA(5¹⁵⁰, 204, F₅, 72) (dual of [204, 54, 73]-code), using

strength reduction [i] based on linear OA(5¹⁵⁰, 204, F₅, 73) (dual of [204, 54, 74]-code), using
- concatenation of two codes [i] based on
  1. linear OA(25⁴¹, 68, F₂₅, 36) (dual of [68, 27, 37]-code), using
    - constructionÂ X applied to AG(F,28P) âŠ‚ AG(F,30P) [i] based on
      1. linear OA(25⁴⁰, 65, F₂₅, 36) (dual of [65, 25, 37]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
        a function field by GarcÃa and Quoos [i]
      2. linear OA(25³⁸, 65, F₂₅, 34) (dual of [65, 27, 35]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
      3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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.