MinT - Information on Result #2691894

Information on Result #2691894

Linear OOA(4²³², 546, F₄, 3, 61) (dual of [(546, 3), 1406, 62]-NRT-code), using 4¹ times duplication based on linear OOA(4²³¹, 546, F₄, 3, 61) (dual of [(546, 3), 1407, 62]-NRT-code), using

trace code [i] based on linear OOA(64⁷⁷, 182, F₆₄, 3, 61) (dual of [(182, 3), 469, 62]-NRT-code), using
- constructionÂ X applied to AG(3;F,466P) âŠ‚ AG(3;F,476P) [i] based on
  1. linear OOA(64⁶⁸, 176, F₆₄, 3, 61) (dual of [(176, 3), 460, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,466P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁵⁸, 176, F₆₄, 3, 51) (dual of [(176, 3), 470, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,476P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁹, 6, F₆₄, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁹, 64, F₆₄, 3, 9) (dual of [(64, 3), 183, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;183,64) [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.