MinT - Information on Result #2505025

Information on Result #2505025

Linear OOA(5¹⁴⁵, 410, F₅, 2, 41) (dual of [(410, 2), 675, 42]-NRT-code), using 5¹ times duplication based on linear OOA(5¹⁴⁴, 410, F₅, 2, 41) (dual of [(410, 2), 676, 42]-NRT-code), using

trace code [i] based on linear OOA(25⁷², 205, F₂₅, 2, 41) (dual of [(205, 2), 338, 42]-NRT-code), using
- constructionÂ X applied to AG(2;F,356P) âŠ‚ AG(2;F,363P) [i] based on
  1. linear OOA(25⁶⁶, 199, F₂₅, 2, 41) (dual of [(199, 2), 332, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,356P) [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(25⁵⁹, 199, F₂₅, 2, 34) (dual of [(199, 2), 339, 35]-NRT-code), using algebraic-geometric NRT-code AG(2;F,363P) [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200 (see above)
  3. linear OOA(25⁶, 6, F₂₅, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁶, 25, F₂₅, 2, 6) (dual of [(25, 2), 44, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;44,25) [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.