MinT - Information on Result #2217585

Information on Result #2217585

Linear OA(16¹³⁰, 136, F₁₆, 111) (dual of [136, 6, 112]-code), using strength reduction based on linear OA(16¹³⁰, 136, F₁₆, 112) (dual of [136, 6, 113]-code), using

juxtaposition [i] based on
1. linear OA(16⁵⁷, 63, F₁₆, 52) (dual of [63, 6, 53]-code), using
  - 2 times truncation [i] based on linear OA(16⁵⁹, 65, F₁₆, 54) (dual of [65, 6, 55]-code), using
    - constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,10P) [i] based on
      1. 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, using the Hermitian function field over F₁₆ [i]
      2. linear OA(16⁵⁸, 64, F₁₆, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) 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]
2. linear OA(16⁶⁷, 73, F₁₆, 59) (dual of [73, 6, 60]-code), using
  - constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,10P) [i] based on
    1. linear OA(16⁶², 64, F₁₆, 59) (dual of [64, 2, 60]-code), using algebraic-geometric code AG(F,4P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    2. linear OA(16⁵⁸, 64, F₁₆, 53) (dual of [64, 6, 54]-code) (see above)
    3. linear OA(16⁵, 9, F₁₆, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,16)), using
      - discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
        Reedâ€“Solomon code RS(11,16) [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.