MinT - Information on Result #859926

Information on Result #859926

Linear OOA(16¹⁰⁸, 66, F₁₆, 2, 72) (dual of [(66, 2), 24, 73]-NRT-code), using OOA 2-folding based on linear OA(16¹⁰⁸, 132, F₁₆, 72) (dual of [132, 24, 73]-code), using

juxtaposition [i] based on
1. linear OA(16⁴¹, 65, F₁₆, 35) (dual of [65, 24, 36]-code), using
  - extended algebraic-geometric code AG_e(F,29P) [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(16⁴³, 67, F₁₆, 36) (dual of [67, 24, 37]-code), using
  - constructionÂ X applied to AG(F,27P) âŠ‚ AG(F,29P) [i] based on
    1. linear OA(16⁴², 64, F₁₆, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    2. linear OA(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 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.