MinT - Information on Result #2514417

Information on Result #2514417

Linear OOA(9¹⁴⁹, 746, F₉, 2, 54) (dual of [(746, 2), 1343, 55]-NRT-code), using 9¹ times duplication based on linear OOA(9¹⁴⁸, 746, F₉, 2, 54) (dual of [(746, 2), 1344, 55]-NRT-code), using

trace code [i] based on linear OOA(81⁷⁴, 373, F₈₁, 2, 54) (dual of [(373, 2), 672, 55]-NRT-code), using
- constructionÂ X applied to AG(2;F,683P) âŠ‚ AG(2;F,688P) [i] based on
  1. linear OOA(81⁷⁰, 369, F₈₁, 2, 54) (dual of [(369, 2), 668, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,683P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(81⁶⁵, 369, F₈₁, 2, 49) (dual of [(369, 2), 673, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,688P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁴, 4, F₈₁, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 81, F₈₁, 2, 4) (dual of [(81, 2), 158, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;158,81) [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.