MinT - Information on Result #860681

Information on Result #860681

Linear OOA(16¹³⁰, 69, F₁₆, 2, 108) (dual of [(69, 2), 8, 109]-NRT-code), using OOA 2-folding based on linear OA(16¹³⁰, 138, F₁₆, 108) (dual of [138, 8, 109]-code), using

juxtaposition [i] based on
1. linear OA(16⁶⁰, 68, F₁₆, 53) (dual of [68, 8, 54]-code), using
  - constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,13P) [i] based on
    1. 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, using the Hermitian function field over F₁₆ [i]
    2. linear OA(16⁵⁶, 64, F₁₆, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16², 4, F₁₆, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,16)), using
      - discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [i]
2. linear OA(16⁶², 70, F₁₆, 54) (dual of [70, 8, 55]-code), using
  - constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,13P) [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 (see above)
    2. linear OA(16⁵⁶, 64, F₁₆, 50) (dual of [64, 8, 51]-code) (see above)
    3. linear OA(16³, 6, F₁₆, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,16) or 6-cap in PG(2,16)), using
      - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [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.