MinT - Information on Result #2513958

Information on Result #2513958

Linear OOA(9¹²⁹, 750, F₉, 2, 42) (dual of [(750, 2), 1371, 43]-NRT-code), using 9¹ times duplication based on linear OOA(9¹²⁸, 750, F₉, 2, 42) (dual of [(750, 2), 1372, 43]-NRT-code), using

trace code [i] based on linear OOA(81⁶⁴, 375, F₈₁, 2, 42) (dual of [(375, 2), 686, 43]-NRT-code), using
- constructionÂ X applied to AG(2;F,695P) âŠ‚ AG(2;F,702P) [i] based on
  1. linear OOA(81⁵⁸, 369, F₈₁, 2, 42) (dual of [(369, 2), 680, 43]-NRT-code), using algebraic-geometric NRT-code AG(2;F,695P) [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(81⁵¹, 369, F₈₁, 2, 35) (dual of [(369, 2), 687, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,702P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁶, 6, F₈₁, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁶, 81, F₈₁, 2, 6) (dual of [(81, 2), 156, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;156,81) [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.