MinT - Information on Result #2700365

Information on Result #2700365

Linear OOA(8¹¹¹, 364, F₈, 3, 39) (dual of [(364, 3), 981, 40]-NRT-code), using 8¹ times duplication based on linear OOA(8¹¹⁰, 364, F₈, 3, 39) (dual of [(364, 3), 982, 40]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁵, 182, F₆₄, 3, 39) (dual of [(182, 3), 491, 40]-NRT-code), using
- constructionÂ X applied to AG(3;F,488P) âŠ‚ AG(3;F,498P) [i] based on
  1. linear OOA(64⁴⁶, 176, F₆₄, 3, 39) (dual of [(176, 3), 482, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,488P) [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(64³⁶, 176, F₆₄, 3, 29) (dual of [(176, 3), 492, 30]-NRT-code), using algebraic-geometric NRT-code AG(3;F,498P) [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.