MinT - Information on Result #2701277

Information on Result #2701277

Linear OOA(8¹⁶⁹, 368, F₈, 3, 65) (dual of [(368, 3), 935, 66]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁶⁸, 368, F₈, 3, 65) (dual of [(368, 3), 936, 66]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁴, 184, F₆₄, 3, 65) (dual of [(184, 3), 468, 66]-NRT-code), using
- constructionÂ X applied to AG(3;F,462P) âŠ‚ AG(3;F,475P) [i] based on
  1. linear OOA(64⁷², 176, F₆₄, 3, 65) (dual of [(176, 3), 456, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,462P) [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(64⁵⁹, 176, F₆₄, 3, 52) (dual of [(176, 3), 469, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,475P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹², 8, F₆₄, 3, 12) (dual of [(8, 3), 12, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹², 64, F₆₄, 3, 12) (dual of [(64, 3), 180, 13]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;180,64) [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.