MinT - Information on Result #2669586

Information on Result #2669586

Linear OOA(2¹²⁷, 70, F₂, 3, 44) (dual of [(70, 3), 83, 45]-NRT-code), using 2¹ times duplication based on linear OOA(2¹²⁶, 70, F₂, 3, 44) (dual of [(70, 3), 84, 45]-NRT-code), using

trace code [i] based on linear OOA(4⁶³, 35, F₄, 3, 44) (dual of [(35, 3), 42, 45]-NRT-code), using
- constructionÂ X applied to AG(3;F,51P) âŠ‚ AG(3;F,56P) [i] based on
  1. linear OOA(4⁵⁹, 32, F₄, 3, 44) (dual of [(32, 3), 37, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,51P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁵⁴, 32, F₄, 3, 39) (dual of [(32, 3), 42, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,56P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [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.