MinT - Information on Result #2513876

Information on Result #2513876

Linear OOA(9¹²⁷, 752, F₉, 2, 40) (dual of [(752, 2), 1377, 41]-NRT-code), using 9¹ times duplication based on linear OOA(9¹²⁶, 752, F₉, 2, 40) (dual of [(752, 2), 1378, 41]-NRT-code), using

trace code [i] based on linear OOA(81⁶³, 376, F₈₁, 2, 40) (dual of [(376, 2), 689, 41]-NRT-code), using
- constructionÂ X applied to AG(2;F,697P) âŠ‚ AG(2;F,705P) [i] based on
  1. linear OOA(81⁵⁶, 369, F₈₁, 2, 40) (dual of [(369, 2), 682, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,697P) [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(81⁴⁸, 369, F₈₁, 2, 32) (dual of [(369, 2), 690, 33]-NRT-code), using algebraic-geometric NRT-code AG(2;F,705P) [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370 (see above)
  3. linear OOA(81⁷, 7, F₈₁, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁷, 81, F₈₁, 2, 7) (dual of [(81, 2), 155, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;155,81) [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.