MinT - Information on Result #2500661

Information on Result #2500661

Linear OOA(4¹⁶³, 134, F₄, 2, 72) (dual of [(134, 2), 105, 73]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁶², 134, F₄, 2, 72) (dual of [(134, 2), 106, 73]-NRT-code), using

trace code [i] based on linear OOA(16⁸¹, 67, F₁₆, 2, 72) (dual of [(67, 2), 53, 73]-NRT-code), using
- constructionÂ X applied to AG(2;F,55P) âŠ‚ AG(2;F,59P) [i] based on
  1. linear OOA(16⁷⁸, 64, F₁₆, 2, 72) (dual of [(64, 2), 50, 73]-NRT-code), using algebraic-geometric NRT-code AG(2;F,55P) [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(16⁷⁴, 64, F₁₆, 2, 68) (dual of [(64, 2), 54, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,59P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (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.