MinT - Information on Result #2501371

Information on Result #2501371

Linear OOA(4²⁵⁹, 454, F₄, 2, 86) (dual of [(454, 2), 649, 87]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁵⁸, 454, F₄, 2, 86) (dual of [(454, 2), 650, 87]-NRT-code), using

trace code [i] based on linear OOA(16¹²⁹, 227, F₁₆, 2, 86) (dual of [(227, 2), 325, 87]-NRT-code), using
- constructionÂ X applied to AG(2;F,361P) âŠ‚ AG(2;F,365P) [i] based on
  1. linear OOA(16¹²⁶, 224, F₁₆, 2, 86) (dual of [(224, 2), 322, 87]-NRT-code), using algebraic-geometric NRT-code AG(2;F,361P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(16¹²², 224, F₁₆, 2, 82) (dual of [(224, 2), 326, 83]-NRT-code), using algebraic-geometric NRT-code AG(2;F,365P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16³, 3, F₁₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16³, 16, F₁₆, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;29,16) [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.