MinT - Information on Result #2498713

Information on Result #2498713

Linear OOA(4¹³³, 148, F₄, 2, 50) (dual of [(148, 2), 163, 51]-NRT-code), using 4¹ times duplication based on linear OOA(4¹³², 148, F₄, 2, 50) (dual of [(148, 2), 164, 51]-NRT-code), using

trace code [i] based on linear OOA(16⁶⁶, 74, F₁₆, 2, 50) (dual of [(74, 2), 82, 51]-NRT-code), using
- constructionÂ X applied to AG(2;F,77P) âŠ‚ AG(2;F,88P) [i] based on
  1. linear OOA(16⁵⁶, 64, F₁₆, 2, 50) (dual of [(64, 2), 72, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,77P) [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 OOA(16⁴⁵, 64, F₁₆, 2, 39) (dual of [(64, 2), 83, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,88P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16¹⁰, 10, F₁₆, 2, 10) (dual of [(10, 2), 10, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16¹⁰, 16, F₁₆, 2, 10) (dual of [(16, 2), 22, 11]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;22,16) [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.