MinT - Information on Result #2510209

Information on Result #2510209

Linear OOA(8¹²³, 372, F₈, 2, 44) (dual of [(372, 2), 621, 45]-NRT-code), using 8¹ times duplication based on linear OOA(8¹²², 372, F₈, 2, 44) (dual of [(372, 2), 622, 45]-NRT-code), using

trace code [i] based on linear OOA(64⁶¹, 186, F₆₄, 2, 44) (dual of [(186, 2), 311, 45]-NRT-code), using
- constructionÂ X applied to AG(2;F,307P) âŠ‚ AG(2;F,318P) [i] based on
  1. linear OOA(64⁵¹, 176, F₆₄, 2, 44) (dual of [(176, 2), 301, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,307P) [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(64⁴⁰, 176, F₆₄, 2, 33) (dual of [(176, 2), 312, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,318P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹⁰, 10, F₆₄, 2, 10) (dual of [(10, 2), 10, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹⁰, 64, F₆₄, 2, 10) (dual of [(64, 2), 118, 11]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;118,64) [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.