MinT - Information on Result #981178

Information on Result #981178

Linear OOA(8¹¹⁶, 186, F₈, 3, 41) (dual of [(186, 3), 442, 42]-NRT-code), using OOA 2-folding based on linear OOA(8¹¹⁶, 372, F₈, 2, 41) (dual of [(372, 2), 628, 42]-NRT-code), using

trace code [i] based on linear OOA(64⁵⁸, 186, F₆₄, 2, 41) (dual of [(186, 2), 314, 42]-NRT-code), using
- constructionÂ X applied to AG(2;F,310P) âŠ‚ AG(2;F,321P) [i] based on
  1. linear OOA(64⁴⁸, 176, F₆₄, 2, 41) (dual of [(176, 2), 304, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,310P) [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(64³⁷, 176, F₆₄, 2, 30) (dual of [(176, 2), 315, 31]-NRT-code), using algebraic-geometric NRT-code AG(2;F,321P) [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.