MinT - Information on Result #2704175

Information on Result #2704175

Linear OOA(9¹⁴⁷, 746, F₉, 3, 51) (dual of [(746, 3), 2091, 52]-NRT-code), using 9¹ times duplication based on linear OOA(9¹⁴⁶, 746, F₉, 3, 51) (dual of [(746, 3), 2092, 52]-NRT-code), using

trace code [i] based on linear OOA(81⁷³, 373, F₈₁, 3, 51) (dual of [(373, 3), 1046, 52]-NRT-code), using
- constructionÂ X applied to AG(3;F,1055P) âŠ‚ AG(3;F,1062P) [i] based on
  1. linear OOA(81⁶⁷, 369, F₈₁, 3, 51) (dual of [(369, 3), 1040, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1055P) [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(81⁶⁰, 369, F₈₁, 3, 44) (dual of [(369, 3), 1047, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1062P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁶, 4, F₈₁, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁶, 81, F₈₁, 3, 6) (dual of [(81, 3), 237, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;237,81) [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.