MinT - Information on Result #858030

Information on Result #858030

Linear OOA(16⁴⁶, 35, F₁₆, 2, 37) (dual of [(35, 2), 24, 38]-NRT-code), using OOA 2-folding based on linear OA(16⁴⁶, 70, F₁₆, 37) (dual of [70, 24, 38]-code), using

discarding factors / shortening the dual code based on linear OA(16⁴⁶, 71, F₁₆, 37) (dual of [71, 25, 38]-code), using
- constructionÂ X applied to AG(F,26P) âŠ‚ AG(F,30P) [i] based on
  1. linear OA(16⁴³, 64, F₁₆, 37) (dual of [64, 21, 38]-code), using algebraic-geometric code AG(F,26P) [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(16³⁹, 64, F₁₆, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-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.