MinT - Information on Result #859982

Information on Result #859982

Linear OOA(16⁸⁴, 44, F₁₆, 2, 74) (dual of [(44, 2), 4, 75]-NRT-code), using OOA 2-folding based on linear OA(16⁸⁴, 88, F₁₆, 74) (dual of [88, 4, 75]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸⁴, 89, F₁₆, 74) (dual of [89, 5, 75]-code), using
- juxtaposition [i] based on
  1. linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
    - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
  2. linear OA(16⁶⁰, 65, F₁₆, 55) (dual of [65, 5, 56]-code), using
    - constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [i] based on
      1. linear OA(16⁶⁰, 64, F₁₆, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F₁₆ [i]
      2. linear OA(16⁵⁹, 64, F₁₆, 54) (dual of [64, 5, 55]-code), using algebraic-geometric code AG(F,9P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.