MinT - Information on Result #982536

Information on Result #982536

Linear OOA(8¹⁶⁸, 184, F₈, 3, 69) (dual of [(184, 3), 384, 70]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁶⁸, 368, F₈, 2, 69) (dual of [(368, 2), 568, 70]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁴, 184, F₆₄, 2, 69) (dual of [(184, 2), 284, 70]-NRT-code), using
- constructionÂ X applied to AG(2;F,282P) âŠ‚ AG(2;F,291P) [i] based on
  1. linear OOA(64⁷⁶, 176, F₆₄, 2, 69) (dual of [(176, 2), 276, 70]-NRT-code), using algebraic-geometric NRT-code AG(2;F,282P) [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(64⁶⁷, 176, F₆₄, 2, 60) (dual of [(176, 2), 285, 61]-NRT-code), using algebraic-geometric NRT-code AG(2;F,291P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64⁸, 8, F₆₄, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁸, 64, F₆₄, 2, 8) (dual of [(64, 2), 120, 9]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;120,64) [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.