MinT - Information on Result #2513802

Information on Result #2513802

Linear OOA(9¹²⁵, 754, F₉, 2, 38) (dual of [(754, 2), 1383, 39]-NRT-code), using 9¹ times duplication based on linear OOA(9¹²⁴, 754, F₉, 2, 38) (dual of [(754, 2), 1384, 39]-NRT-code), using

trace code [i] based on linear OOA(81⁶², 377, F₈₁, 2, 38) (dual of [(377, 2), 692, 39]-NRT-code), using
- constructionÂ X applied to AG(2;F,699P) âŠ‚ AG(2;F,708P) [i] based on
  1. linear OOA(81⁵⁴, 369, F₈₁, 2, 38) (dual of [(369, 2), 684, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,699P) [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(81⁴⁵, 369, F₈₁, 2, 29) (dual of [(369, 2), 693, 30]-NRT-code), using algebraic-geometric NRT-code AG(2;F,708P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁸, 8, F₈₁, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁸, 81, F₈₁, 2, 8) (dual of [(81, 2), 154, 9]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;154,81) [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.