MinT - Information on Result #964356

Information on Result #964356

Linear OOA(4¹¹², 71, F₄, 3, 43) (dual of [(71, 3), 101, 44]-NRT-code), using OOA 2-folding based on linear OOA(4¹¹², 142, F₄, 2, 43) (dual of [(142, 2), 172, 44]-NRT-code), using

trace code [i] based on linear OOA(16⁵⁶, 71, F₁₆, 2, 43) (dual of [(71, 2), 86, 44]-NRT-code), using
- constructionÂ X applied to AG(2;F,84P) âŠ‚ AG(2;F,92P) [i] based on
  1. linear OOA(16⁴⁹, 64, F₁₆, 2, 43) (dual of [(64, 2), 79, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,84P) [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(16⁴¹, 64, F₁₆, 2, 35) (dual of [(64, 2), 87, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,92P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁷, 7, F₁₆, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁷, 16, F₁₆, 2, 7) (dual of [(16, 2), 25, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;25,16) [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.