MinT - Information on Result #2498229

Information on Result #2498229

Linear OOA(4¹³³, 158, F₄, 2, 45) (dual of [(158, 2), 183, 46]-NRT-code), using 4¹ times duplication based on linear OOA(4¹³², 158, F₄, 2, 45) (dual of [(158, 2), 184, 46]-NRT-code), using

trace code [i] based on linear OOA(16⁶⁶, 79, F₁₆, 2, 45) (dual of [(79, 2), 92, 46]-NRT-code), using
- constructionÂ X applied to AG(2;F,82P) âŠ‚ AG(2;F,98P) [i] based on
  1. linear OOA(16⁵¹, 64, F₁₆, 2, 45) (dual of [(64, 2), 77, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,82P) [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(16³⁵, 64, F₁₆, 2, 29) (dual of [(64, 2), 93, 30]-NRT-code), using algebraic-geometric NRT-code AG(2;F,98P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16¹⁵, 15, F₁₆, 2, 15) (dual of [(15, 2), 15, 16]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16¹⁵, 16, F₁₆, 2, 15) (dual of [(16, 2), 17, 16]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;17,16) [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.